case study questions on playing with numbers for class 6

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Case Study Questions for Class 6 Maths Chapter 3 Playing with Numbers

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Here in this article, we are providing case study questions for class 6 maths. Here you will find case study questions for class 6 maths Chapter 3 Playing with Numbers .

Case Study Question 1:

A florist had 200 roses, 180 marigold and 320 orchids with him. He was asked to make garlands of flowers with only roses or only marigold or only orchids each containing the some number of flowers.

(i) The correct prime factorisation of 180 is: (a) 2 x 2 x 3 x 3 x 5 (b) 4 x 3 x 3 x 5 (c) 2 x 2 x 9 x 5 (d) 4 x 9 x 5

Ans. Option (a) is correct. Explanation: Option (a) has all the factors prime numbers. So it is the correct factorisation of 180.

(ii) The LCM of two coprime numbers is equal to (a) 1 (b) the greatest number (c) their product (d) odd

Ans. Option (c) is correct. Explanation: The LCM of two coprime numbers is their product.

(iii) What will be the largest number of flowers he can join together without leaving a single flower. Sol. We should find the greatest number that is the HCF of 200,180 and 320.

case study questions on playing with numbers for class 6

200 = 2 × 2 × 2 × 5 × 5 180 = 2 × 2 × 3 × 3 × 5 320 = 2 × 2 × 2 × 2 × 2 × 2 × 5 HCF = 2 × 2 × 5 = 20 Hence largest number of flowers is 20.

(iv) Find the LCM of 200 and 180.

LCM = 2 × 2 × 2 × 5 × 5 × 3 × 3 = 1800

Maths Class 6 Chapter List

Latest chapter list (2023-24).

Chapter 1 Knowing Our Numbers Case Study Questions Chapter 2 Whole Numbers Case Study Questions Chapter 3 Playing with Numbers Case Study Questions Chapter 4 Basic Geometrical Ideas Case Study Questions Chapter 5 Understanding Elementary Shape Case Study Questions Chapter 6 Integers Case Study Questions Chapter 7 Fractions Case Study Questions Chapter 8 Decimals Case Study Questions Chapter 9 Data Handling Case Study Questions Chapter 10 Mensuration Case Study Questions Chapter 11 Algebra Case Study Questions Chapter 12 Ratio and Proportion Case Study Questions

Old Chapter List

Chapter 1 Knowing Our Numbers Chapter 2 Whole Numbers Chapter 3 Playing with Numbers Chapter 4 Basic Geometrical Ideas Chapter 5 Understanding Elementary Shape Chapter 6 Integers Chapter 7 Fractions Chapter 8 Decimals Chapter 9 Data Handling Chapter 10 Mensuration Chapter 11 Algebra Chapter 12 Ratio and Proportion Chapter 13 Symmetry Chapter 14 Practical Geometry

Deleted Chapter:

Tips for Answering Case Study Questions for Class 6 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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Important Questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers

CBSE Class 6 Maths Important Questions Chapter 3 - Playing with Numbers - Free PDF Download

The NCERT Solutions for playing with numbers class 6 important questions are helpful for the exam preparation as it covers all types of questions present across the seven exercises of this chapter. The subject experts have created these important questions for class 6 maths chapter 3 at Vedantu to provide the best possible methods to solve the problems. These CBSE solutions to the questions on playing with numbers for class 6 are the ultimate study material a CBSE Class 6 student can get hold of to score good marks in the Maths Examination. Important questions for class 6 maths chapter 3 discusses the concepts of multiples, divisors, factors, and how to identify factors and multiples along with HCF and LCM.

The class 6 maths chapter 3 important questions talk about factors and multiples, prime and composite numbers, tests for divisibility of numbers, common factors, and common multiples.The problems in this chapter have been divided into 7 exercises for the students to identify the topics easily.

Apart from, playing with numbers class 6 important questions we have notes, question papers, and other learning materials in PDF format, which students can easily download and practice offline as well. Also, solving sample papers as well as previous year question papers will give an idea of the question pattern for Chapter 3 helping them in standing ahead in the exam preparation. Let’s go through the important questions for class 6 maths chapter 3.

You can also register Online for NCERT Class 6 Science and Class 6 Maths tuition on Vedantu.com to score more marks in CBSE board examination.

Download CBSE Class 6 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 6 Maths Important Questions for other chapters:

Study Important Questions for Class 6 Mathematics Chapter 3- Playing with Numbers

Very short answer questions 1 mark.

1. \[2\] is a composite number. True or False

Ans: A number having more than two factors is a Composite number.

The number \[2\] has factors \[2\], $1$.

\[2\] is not a composite number.

Therefore, the statement is False.

2. $1$ is neither prime nor composite. Say True or False.

Ans: Given: A prime number is a number having exactly two positive factors $1$ and the number itself. $1$ is neither prime nor composite.

So, the given statement is true.

3. Prime numbers have more than two factors. Say True or False.

Ans: Given: We know that A prime number is a number having exactly two positive factors $1$ and the number itself.

Therefore, the given statement is False.

4. If a number is a factor of each of the two given numbers, then it must be a factor of their sum. Say True or False.

Ans: Given: If a number is a factor of each of the two given numbers, then it must be a factor of their sum.

For example, $3$ is a factor of $6{\text{ and }}9$.

Their sum is,

$6 + 9 $

$ = 15 $

It is also divisible by $3$.

Therefore, we can see that the statement given is True.

5. The greatest number which is not a common factor of two or more given numbers is called HCF. Say True or False.

Ans: Given: We know that the greatest common factor (GCF) is the greatest common divisor that is common to two or more numbers. However, it is the product of all prime factors common to the numbers.

Therefore, ${\text{GCF = HCF}}$.

Therefore, the given statement is true.

6. Lowest of the common multiple of two or more numbers is called the ______ of the given numbers.

Ans: Given: We know that Lowest of the common multiple of two or more numbers is called the LCM of the given numbers.

Short Answer Questions 2 Mark

1. Write all the factors of \[78.\]

Ans: Given: \[78\]

We need to find all the factors of the given number.

Therefore, factors of \[78\] will be

$1 \times 78 $

$ 2 \times 39 $

$ 3 \times 26 $

$ 6 \times 13 $

So, factors are $1,2,3,6,13,26,39,78$

2. Write the first five multiples of \[7.\]

Ans: Given: $7$

We need to find the first five multiples of the given numbers.

A Multiple of a number is any number that is the product of that number and any other integer.

Therefore, the multiples of $7$ are

$ 7 \times 1 = 7 $

$ 7 \times 2 = 14 $

$ 7 \times 3 = 21 $

$ 7 \times 4 = 28 $

$ 7 \times 5 = 35 $

3. Determine whether the number \[5555\] is divisible by \[5\] and \[10.\]

Ans: Given: We know that a number is divisible by 5 if the unit digit of the number is divisible by \[5\] or it is zero.

Therefore, \[5555\] has unit place \[5\] and it is divisible by \[5\].

A number is divisible by \[10\]if the unit place of the number is zero.

Therefore, the number \[5555\] has a unit place \[5\]. Hence, it is not divisible by \[10.\]

4. Determine whether the number \[1890164\] is divisible by \[2,{\text{ }}4,{\text{ }}6\] and \[8.\]

Ans: Given: \[1890164\]

We need to find if the given number is divisible by \[2,{\text{ }}4,{\text{ }}6\] and \[8.\]

A number is divisible by $2,$ if the unit place of the number is divisible by $2.$

The number \[1890164\] has unit place $4$, so the number is divisible by $2.$

A number is divisible by $4$, if the number formed by tens and one's place is divisible by $4$.

The number \[1890164\] has $64$, so it is divisible by $4$.

A number is divisible by $6$, if it is divisible by $2{\text{ and }}3.$ We can see that the number is divisible by $2.$ It is not divisible by $3$as the sum of digits $1 + 8 + 9 + 0 + 1 + 6 + 4 = 29$ is not divisible by $3.$

Therefore, the number \[1890164\] is not divisible by $6$.

A number is divisible by $8,$ if the number formed by hundreds, tens, and ones digit is divisible by $8.$

Therefore, the number \[1890164\] is not divisible by $8.$

5. Determine whether the number 70169308 is divisible by 11?

Ans: Given: \[70169308\]

We need to find if the given number is divisible by \[11.\]

A number is divisible by $11$if the difference of sum of digits in odd places and sum of digits in even places is divisible by \[11.\]

The digits at odd places are

$ = 8,3,6,0 $

$ {\text{Sum}} = 8 + 3 + 6 + 0 $

$ = 17 $

The digits at even places are

$ = 0,9,1,7 $

$ {\text{Sum}} = 0 + 9 + 1 + 7 $

The difference will be

$ 17 - 17 $

$ = 0 $

Therefore, the number \[70169308\] is divisible by \[11.\]

6. The HCF of two numbers is 18 and their product is 3072. Find the LCM.

Ans: Given: HCF of two numbers \[ = 18\]

Product of the numbers \[ = 3072\]

We need to find the LCM of the numbers.

We know that,

${\text{LCM}} = \dfrac{{{\text{product of given numbers}}}}{{{\text{HCF}}}}$

Therefore, the LCM will be

$ = \dfrac{{3072}}{{18}} $

$ = 170.6 $

$ \approx 171 $

Short Answer Questions 3 Mark

1. Give the prime factorization of \[30580.\]

Ans: Given: \[30580\]

We need to find factors using Prime Factorization.

$\underline{2 \left| \,\,{30580\,\,}\right.} $

$\underline{2 \left|\,\, {15290\quad}\right.} $

$\underline{5 \left| \,\,{7645\quad}\right.} $

$\underline{11 \left| \,\,{1529\quad}\right.} $

$\,\,\,\, \underline{\left| \,\,{139\quad}\right.} $

Therefore, the prime factors will be

$2,2,5,11,139$

2. Reduce \[\mathbf{\dfrac{{279}}{{381}}}\] to lowest forms.

Ans: Given: \[\dfrac{{279}}{{381}}\]

We need to reduce the given fraction to its lowest form.

The lowest fraction will be when the numbers do not have common factors other than $1.$

Therefore, the reduced form of the given number will be

$ \dfrac{{279}}{{381}} \div \dfrac{3}{3} $

$ = \dfrac{{93}}{{127}} $

3. Find the LCM of \[\mathbf{48,{\text{ }}96}\] and \[\mathbf{108.}\] by prime factorization method.

Ans: Given: $48,96,108$

We need to find the LCM of the given numbers.

LCM stands for least common multiple.

So, LCM of the given numbers will be

$\underline{2 \left| \,\,{48,96,108\,\,}\right.} $

$\underline{2 \left|\,\, {24,48,54\quad}\right.} $

$\underline{2 \left| \,\,{12,24,27\quad}\right.} $

$\underline{2 \left| \,\,{6,12,27\quad}\right.} $

$\underline{3 \left| \,\,{3,6,27\quad}\right.} $

$\,\,\,\, \underline{\left| \,\,{1,2,9\quad}\right.} $

$\therefore {\text{LCM}} = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 $

$ = 864 $

4. Find LCM of \[\mathbf{8,{\text{ }}18,{\text{ }}27,{\text{ }}36}\] by division method.

Ans: Given: \[8,{\text{ }}18,{\text{ }}27,{\text{ }}36\]

We need to find the LCM of the given numbers using the division method.

$\underline{2 \left| \,\,{8,18,27,36\,\,}\right.} $

$\underline{2 \left|\,\, {4,9,27,18\quad}\right.} $

$\underline{3 \left| \,\,{2,9,27,9\quad}\right.} $

$\underline{3 \left| \,\,{2,3,9,3\quad}\right.} $

$\,\,\,\, \underline{\left| \,\,{2,1,3,1\quad}\right.} $

$ \therefore LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 3$

$ = 216 $

Long Answer Questions 4 Mark

1. Determine whether 64275 and 65403are divisible by 3 and 9 respectively.

Ans: Given: \[64275\], \[65403\]

We need to find if \[64275\] is divisible by \[3\] and \[65403\] is divisible by \[9\].

A number is divisible by \[3\] if the sum of its digits is divisible by\[3\].

Sum of digits of \[64275\] is

$ 6 + 4 + 2 + 7 + 5 $

$ = 24 $

This is divisible by \[3\]. Therefore, the number is divisible by \[3\].

A number is divisible by \[9\] if the sum of its digits is divisible by \[9\].

Sum of digits of \[65403\] is

$ 6 + 5 + 4 + 0 + 3 $

$ = 18 $

This is divisible by \[9\]. Therefore, the number is divisible by \[9\].

2. Find the HCF and LCM of 496 and 2080 by prime factorization or division method.

Ans: Given: \[496\], \[2080\]

We need to find the LCM and HCF of the given numbers by prime factorization or division method.

We know that

${\text{LCM}} = \dfrac{{{\text{product of the numbers}}}}{{{\text{HCF}}}}$

The HCF of the given numbers will be

$\quad \,\,\,\,\,\, 4$

$496{\overline{)\,\,{2080}\quad}}$

$\quad\underline{\,1984\,\,} $

$\,\,\,\,\, 96{\overline{)\,\,{496}{(5}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,480\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 16{\overline{)\,\,{96}{(6}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,96\,\,} $

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,0\,\,} $

Therefore, ${\text{HCF}} = 16$

The LCM of the given numbers using the formula given above will be

$= \dfrac{{496 \times 2080}}{{16}} $

$ = 31 \times 2080 $

$ = 64,480 $

3. Find HCF by division method for 613and 893.

Ans: Given: The numbers \[613\], \[893\]

We need to find the HCF of the given numbers using the division method.

Therefore, HCF by division method will be

$\quad \,\,\,\,\,\, 1$

$613{\overline{)\,\,{893}\quad}}$

$\quad\underline{\,613\,\,} $

$\,\,\,\,\, 280{\overline{)\,\,{613}{(2}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,560\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 53{\overline{)\,\,{280}{(5}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,265\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 15{\overline{)\,\,{53}{(3}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,45\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 8{\overline{)\,\,{15}{(1}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,8\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 7{\overline{)\,\,{8}{(1}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,7\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 1{\overline{)\,\,{7}{(7}\quad}}$

Therefore, the HCF of the given numbers will be $1.$

4. Find HCF of \[\mathbf{138,{\text{ }}180,{\text{ }}260.}\]

Ans: Given: \[138,{\text{ }}180,{\text{ }}260\]

We need to find the HCF of the given numbers.

First, find the factors and then HCF.

Factors of $138$ will be

$\underline{2 \left| \,\,{138\,\,}\right.} $

$\underline{3 \left|\,\, {69\quad}\right.} $

$\underline{23 \left| \,\,{23\quad}\right.} $

$\,\,\,\, \underline{\left| \,\,{1\quad}\right.} $

$ 138 = 2 \times 3 \times 23 $

Factors of $180$ will be

$\underline{2 \left| \,\,{180\,\,}\right.} $

$\underline{2 \left|\,\, {90\quad}\right.} $

$\underline{3 \left| \,\,{45\quad}\right.} $

$\underline{3 \left| \,\,{15\quad}\right.} $

$\underline{5 \left| \,\,{5\quad}\right.} $

$180$ = $2 \times 2 \times 5 \times 3 \times 3$

= ${2^2} \times {3^2} \times 5$

The factors of $260$ will be

$\underline{2 \left| \,\,{260\,\,}\right.} $

$\underline{2 \left|\,\, {130\quad}\right.} $

$\underline{5 \left| \,\,{65\quad}\right.} $

$\underline{13 \left| \,\,{13\quad}\right.} $

$260$ = $2 \times 2 \times 5 \times 13$

= ${2^2} \times 5 \times 13$ Therefore, HCF of the given numbers will be the factors common in each number.

5. The circumferences of three tyres are \[\mathbf{40,{\text{ }}50}\] and \[\mathbf{70{\text{ cm}}{\text{.}}}\] If they moving simultaneously, then what is the least distance they should cover before they make one revolution?

Ans: Given: circumferences of three tyres are \[40,{\text{ }}50\] and \[70{\text{ cm}}\]

We need to find the least distance covered by the tyres before they make one revolution.

We will find the LCM of the circumference given and that will be the distance covered by the tyres.

Therefore, the least distance covered by the tyres before they make one revolution will be

$\underline{2 \left|\,\, {40,50,70\quad}\right.} $

$\underline{2 \left| \,\,{20,25,35\quad}\right.} $

$\underline{5 \left| \,\,{10,25,35\quad}\right.} $

$\underline{5 \left| \,\,{2,5,7\quad}\right.} $

$\text{LCM}$ = $2 \times 2 \times 2 \times 5 \times 5 \times 7$

= $1400 {\text{cm}}$

Very Long Answer Questions 5 Mark

1. The length, breadth and height of the cuboid is \[45,{\text{ }}85\] and \[115{\text{ cm}}\] respectively. Find the length of the longest tape which can measure the three dimensions exactly.

Ans: Given: length of cuboid $ = 45$

Breadth of cuboid $ = 85$

Height of cuboid $ = 115$

We need to find the length of the longest tape which can measure the three dimensions exactly.

For this, find the HCF and the HCF found will be the length of the Tape.

HCF of $45{\text{ and }}85$

$45{\overline{)\,\,{85}\quad}}$

$\quad\underline{\,45\,\,} $

$\,\,\,\,\, 40{\overline{)\,\,{45}{(1}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,40\,\,} $

$\,\,\,\,\,\,\,\,\,\,\,\, 5{\overline{)\,\,{40}{(8}\quad}}$

$\,\,\,\,\, \underline{\,\,\,\,\,\,\,\,\,\,40\,\,} $

$ {\text{HCF}} = 5 $

Now, we will find HCF of $5,115$

$\quad \,\,\,\,\,\, 23$

$5{\overline{)\,\,{115}\quad}}$

$\quad\underline{\,10\,\,} $

$\,\,\,\,\, \underline{\,\,\,\,\,\,15\,\,} $

$\,\,\,\,\,\,\, \underline{\,\,\,\,\,\,0\,\,} $

Therefore, the length of the tape which can measure the three dimensions exactly $ = d$

2. What is the least number to be subtracted from 1045 to get a number exactly divisible by 22?

Ans: Given: Number \[1045\]

To find: the least number to be subtracted from \[1045\] to get a number exactly divisible by \[22.\]

Divide the given number with \[22.\] The remainder will be the required number.

Therefore,

$\quad \,\,\,\,\,\, 47$

$22{\overline{)\,\,{1045}\quad}}$

$\quad\underline{\,88\,\,} $

$\,\,\,\,\, \underline{\,\,\,\,\,\,165\,\,} $

$\,\,\,\,\,\,\, \underline{\,\,\,\,\,\,154\,\,} $

$\,\,\,\,\,\,\, \underline{\,\,\,\,\,\,11\,\,} $

So, the least number to be subtracted from \[1045\] to get a number exactly divisible by \[22\] is $11.$

Important Questions for Class 6 Maths Chapter 3

Question 1. What will be the sum of any two (a) Odd numbers? (b) Even numbers?

Let’s take any two numbers. The sum of any two given odd numbers is even numbers.

Examples: 5 + 3 = 8

15 + 13 = 28

The sum of any two given even numbers is an even number

Examples: 2 + 8 = 10

12 + 28 = 40

Question 2. The numbers 13 and 31 are prime numbers. Both these numbers have the same digits that are 1 and 3. Find such pairs of prime numbers upto 100.

Solution:

The prime numbers with the same digits upto 100 are as follows:

These are some important questions for class 6 maths chapter 3.

Reasons Why Choose Vedantu's Important Questions Pdf

The questions are comprehensive. Vedantu's important questions PDF covers all the important concepts in the chapter. This means that you can be confident that you are prepared for any question that comes up in the exam.

The questions are challenging. The questions in Vedantu's important questions PDF are not just easy to answer. They are challenging enough to test your understanding of the concepts. This will help you to learn the concepts more deeply and be better prepared for the exam.

The questions are relevant to the latest exam pattern. Vedantu's important questions PDF is updated regularly to ensure that the questions are relevant to the latest exam pattern. This means that you can be confident that you are practicing with questions that are similar to the ones that you will see in the exam.

The questions are accompanied by solutions. Each question in Vedantu's important questions PDF is accompanied by a solution. This means that you can check your answers and learn from your mistakes.

The PDF is easy to download and use. Vedantu's important questions PDF is available for free download. You can download it and use it on your computer, tablet, or smartphone.

Overall, Vedantu's important questions PDF is a valuable resource for students who are preparing for the CBSE board exams. The questions are comprehensive, challenging, relevant, and accompanied by solutions. This makes them an effective way to practice and improve your understanding of the concepts.

How Class 6 Playing with Numbers Questions are Crucial for Preparation?

By referring to CBSE class 6 maths Playing with Numbers important questions , students can stay ahead of the competition.

They can practice important questions and recognize their mistakes.

Students can make notes and highlight the vital information based on these questions.

By solving the important questions, the students can revise the Playing with Numbers topic very well.

These crucial questions are also valuable to help solve their homework problems.

The questions will allow students to understand various sums given in this Playing with Numbers chapter.

Overall, these important questions serve as a resourceful study guide for the students.

Important Related Links for CBSE Class 6 Maths

Vedantu's collection of Important Questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers proves to be a valuable resource for students seeking comprehensive understanding and practice in this subject. Through a well-structured and meticulously curated set of questions, Vedantu facilitates a deeper grasp of mathematical concepts, aiding students in developing problem-solving skills and boosting their confidence. The platform's emphasis on practical applications and real-life scenarios enhances students' critical thinking abilities, making learning an engaging experience. With Vedantu's support, students can excel in their academic pursuits, laying a strong foundation for future mathematical challenges and nurturing a genuine love for the subject.

FAQs on Important Questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers

1. How many exercises are there in Chapter 3 of NCERT Solutions for Class 6 Maths?

There are 7 exercises in Chapter 3 of NCERT Solutions for Class 6 Maths. The number of questions in each exercise is mentioned below.

Exercise 3.1: Divisibility Rules (4 Questions)

Exercise 3.2: Prime Numbers (12 Questions)

Exercise 3.3: Factors and Multiples (5 Questions)

Exercise 3.4: HCF and LCM (7 Questions)

Exercise 3.5: Venn Diagrams (12 Questions)

Exercise 3.6: More on HCF and LCM (4 Questions)

Exercise 3.7: Challenging Problems (11 Questions)

2. What will I learn about properties of factor in Chapter 3 of NCERT Solutions for Class 6 Maths?

Properties of factors of a number:

1 is a factor of every number.

Every number is a factor of itself.

The product of any two factors of a number is the number itself.

A number has an infinite number of factors if it is a composite number.

A number has only two factors if it is a prime number.

3. What are the types of numbers discussed in Chapter 3 of NCERT Solutions for Class 6 Maths as per the latest CBSE syllabus?

The types of numbers discussed in Chapter 3 of NCERT Solutions for Class 6 Maths as per the latest CBSE syllabus are-

Prime numbers

Even numbers

Odd numbers

Whole numbers

Natural numbers

Composite numbers

4. How can I prepare for the CBSE board exams on this chapter?

Here are some tips on how you can prepare for the CBSE board exams on this chapter:

Study the chapter carefully and understand the concepts.

Solve the practice questions in the NCERT book and other reference books.

Go through the important questions that are asked in the CBSE board exams.

Practice with a variety of questions, including easy, medium, and difficult ones.

Take mock tests to assess your preparation level.

5. Where can I find the important questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers?

On Vedantu (vedantu.com) You can find the important questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers. We provide:

NCERT Notes

Revision Notes

Important Questions

Live videos by our Master Teachers

Study groups

Doubt solving

I hope this helps! Let me know if you have any other questions.

Chapter wise Important Questions for CBSE Class 6 Maths

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

NCERT Solutions for class 6 maths chapter 3 Playing With Numbers will help students study the topics, such as multiples, divisor, factors, and the identification of factors and multiples. In the previous two chapters, we studied whole numbers and natural numbers. With the help of this chapter, we will take a step ahead and learn the meaning of factors and multiples of a number. NCERT Solutions Class 6 maths chapter 3 consists of activities related to these concepts that make learning super easy.

With the help of the exercise questions, students will be able to find out the factors of a number using different methods. They will also be able to comprehend the application of these concepts in their day-to-day lives. Class 6 Maths NCERT Solutions Chapter 3 Playing with Numbers has a total of 7 exercises. With the help of this article, we will do an in-depth analysis of NCERT Solutions Class 6 Maths Chapter 3, and also you can find some of these in the exercises given below.

NCERT Solutions Class 6 Maths Chapter 3 Ex 3.1
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.2
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.3
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.4
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.5
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.6
NCERT Solutions Class 6 Maths Chapter 3 Ex 3.7

NCERT Solutions for Class 6 Maths Chapter 3 PDF

One of the key concepts covered in the NCERT solutions class 6 maths is finding the factors of a number in a stepwise manner. The only way students can get a good grasp of the concepts is by solving all the questions given in this coursebook. The NCERT Solutions for Class 6 Maths Chapter 3 are free to download using the links given below:

☛ Download Class 6 Maths NCERT Solutions Chapter 3 Playing with Numbers

NCERT Class 6 Maths Chapter 3 Download PDF

The best way to get strong fundamentals in maths is by practicing many questions on a regular basis. Thus, students need to visit the above links from time to time and revise all the questions. Numbers are everywhere, be it time, date, year, and weather; we use numerals to count things. We utilize numbers for counting money, measurements , phone numbers, phone passwords, locks, reading, page numbers, and TV channels. Engineers utilize numbers in their calculations when creating structures and roadways. They are also used by doctors to check blood counts and administer medications. With such wide applications of numbers , it is important for us to study the numbers in detail. An elaborate analysis of NCERT Solutions Class 6 Maths Chapter 3 is given below :

Class 6 Maths Chapter 3 Ex 3.1 - 4 Questions
Class 6 Maths Chapter 3 Ex 3.2 - 9 Questions
Class 6 Maths Chapter 3 Ex 3.3 - 6 Questions
Class 6 Maths Chapter 3 Ex 3.4 - 7 Questions
Class 6 Maths Chapter 3 Ex 3.5 - 12 Questions
Class 6 Maths Chapter 3 Ex 3.6 - 3 Questions
Class 6 Maths Chapter 3 Ex 3.7 - 11 Questions

☛ Download Class 6 Maths Chapter 3 NCERT Book

Topics Covered: The topics covered under class 6 maths NCERT solutions chapter 3 are multiples , divisors , factors , identification of multiples, and factors. We will also learn how to determine if a number is prime or composite using the factors. Apart from that, we will explore how to find the HCF and LCM using the factors method.

Total Questions: Class 6 maths chapter 3 Playing with Numbers has 52 questions in total out of which 30 can be classified as easy short answer sums, 15 are long answer type problems while the other 7 are complex problems.

List of Formulas in NCERT Solutions Class 6 Maths Chapter 3

NCERT solutions class 6 maths chapter 3 does not consist of any formulas however there are some important concepts discussed in the chapter related to finding the HCF, LCM, and factors of numbers. We will discuss these essential concepts in this section.

A prime number is any number other than 1 that has only two factors: 1 and the number itself. Composite numbers are those that have more than two factors. Number one is neither composite nor prime.
If two numbers are divisible by a number, their sum and difference are likewise divisible by the same number.
The Highest Common Factor (HCF) of two or more numbers is the highest common factor among them.
The Least Common Multiple (LCM) of two or more numbers is the smallest of their common multiples.

Important Questions for Class 6 Maths NCERT Solutions Chapter 3

Faqs on ncert solutions for class 6 maths chapter 3, why are ncert solutions class 6 maths chapter 3 important.

NCERT solutions class 6 Maths Chapter 3 are designed by subject experts from IIT and Cambridge university. This chapter will help you understand the prime role that different numbers and their multiples play in solving an equation. These solutions also include various questions based on the laws of divisibility which are explained in detail. The NCERT solutions class 6 maths chapter 3 are the perfect study material for class 6 students as it will help them review their answers and also provide a step-wise approach to solve all questions.

Do I Need to Practice all Questions Provided in Class 6 Maths NCERT Solutions Playing with Numbers?

It is crucial for the students to practice all the questions in NCERT Solutions Class 6 Maths Playing With Numbers. This will help them understand the concepts better and build confidence, thus enabling them to memorize formulas faster. The main highlight of this chapter is HCF and LCM, and it is essential to practice all of the questions related to these topics. All the problems cover a variety of subject matter, thus allowing students to get a better grasp of numbers.

What are the Important Topics Covered in NCERT Solutions Class 6 Maths Chapter 3?

All the topics covered in NCERT Solutions Class 6 Maths Chapter 3 are equally important. However, to streamline the studying process, students need to give ample time in preparing questions based on HCF, LCM, and factors. Additionally, they must also go through the entire theory of the chapter to understand the concepts better.

How Many Questions are there in Class 6 Maths NCERT Solutions Chapter 3 Playing With Numbers?

There are 52 questions in the NCERT Solutions Class 6 Maths Chapter 3 Playing With Numbers. These are divided into seven different exercises. Exercise 3.6 and 3.7 are the most important exercises from an examination perspective, covering important topics like the prime factors, HCF, and LCM of numbers. Since these concepts are new to students, they should engage in activities to understand these concepts in a more practical way.

What are the Important Formulas in NCERT Solutions Class 6 Maths Chapter 3?

Students will come across many important concepts in the NCERT Solutions Class 6 maths chapter 3. We do not have any important formulas in this chapter; however certain facts like every number is a factor and multiple will help them understand the prime role that different numbers and their multiples play in solving an equation. Students must go through all the questions and solve the examples in order to develop a rock-solid foundation.

How CBSE Students can utilize NCERT Solutions Class 6 Maths Chapter 3 effectively?

To effectively utilize the NCERT Solutions Class 6 Maths Chapter 3, kids must first go through the theoretical concepts and activities discussed in the chapter. Topics such as common factors and multiples, divisibility laws, greatest common factors, lowest common factors, etc., are introduced to the kids. Students will be able to understand prime and composite numbers, as well as their differences, provided they have a thorough understanding of the chapter. This will help students identify practical ways of solving a problem.

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Unit 3: Playing with numbers

Playing with numbers 3.1.

Finding factors of a number (Opens a modal)
Finding factors and multiples (Opens a modal)
Factors and multiples Get 3 of 4 questions to level up!
Intro to factors and multiples Get 5 of 7 questions to level up!
Playing with numbers 3.1 Get 6 of 8 questions to level up!

Playing with numbers 3.2

Prime numbers (Opens a modal)
Recognizing prime and composite numbers (Opens a modal)
Playing with numbers 3.2 Get 6 of 8 questions to level up!

Playing with numbers 3.3

Divisibility tests for 2, 3, 4, 5, 6, 9, 10 (Opens a modal)
Recognizing divisibility (Opens a modal)
Playing with numbers 3.3 Get 7 of 10 questions to level up!

Playing with numbers 3.4

No videos or articles available in this lesson
Playing with numbers 3.4 Get 5 of 7 questions to level up!

Playing with numbers 3.5

Prime factorization (Opens a modal)
Prime factorization exercise (Opens a modal)
Playing with numbers 3.5 Get 6 of 8 questions to level up!

Playing with numbers 3.6

Greatest common factor examples (Opens a modal)
HCF visualized (Opens a modal)
Playing with numbers 3.6 Get 5 of 6 questions to level up!

Playing with numbers 3.7

Least common multiple (Opens a modal)
LCM visualized (Opens a modal)
Least common multiple: repeating factors (Opens a modal)
Least common multiple of three numbers (Opens a modal)
Playing with numbers 3.7 Get 6 of 8 questions to level up!

NCERT Solutions

NCERT Class 6
NCERT 6 Maths
Chapter 3: Playing With Numbers
Exercise 3.6

NCERT Solutions For Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.6

The NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.6 explains the method of solving problems related to finding the HCF of a given set of numbers. These NCERT Solutions are prepared by the subject experts at BYJU’S to help students ace the exam. Set of examples are available in the NCERT textbook , before the exercise, to help students get a hold of the concepts. The faculty has followed the same method as of the examples to solve the questions present in the exercise. The solutions are created to help students avoid any sort of confusion that could arise while solving the problems. The exercise-wise problems can be solved and revised by the students with the help of the NCERT Solutions Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.6.

Chapter 1 Knowing our Numbers
Chapter 2 Whole Numbers
Chapter 3 Playing With Numbers
Chapter 4 Basic Geometrical Ideas
Chapter 5 Understanding Elementary Shapes
Chapter 6 Integers
Chapter 7 Fractions
Chapter 8 Decimals
Chapter 9 Data Handling
Chapter 10 Mensuration
Chapter 11 Algebra
Chapter 12 Ratio And Proportion
Chapter 13 Introduction To Symmetry
Chapter 14 Practical Geometry
Exercise 3.1 Chapter 3 Playing With Numbers
Exercise 3.2 Chapter 3 Playing With Numbers
Exercise 3.3 Chapter 3 Playing With Numbers
Exercise 3.4 Chapter 3 Playing With Numbers
Exercise 3.5 Chapter 3 Playing With Numbers
Exercise 3.6 Chapter 3 Playing With Numbers
Exercise 3.7 Chapter 3 Playing With Numbers

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.6

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Access NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers Exercise 3.6

1. Find the HCF of the following numbers:

(f) 34, 102

(g) 70, 105, 175

(h) 91, 112, 49

(i) 18, 54, 81

(j) 12, 45, 75

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 1

18 = 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

HCF = 2 × 3 = 6

Therefore, the HCF of 18, 48 is 6

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 3

30 = 2 × 3 × 5

42 = 2 × 3 × 7

Therefore, the HCF of 30, 42 is 6

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 5

60 = 2 × 2 × 3 × 5

Therefore, the HCF of 18, 60 is 6

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 7

27 = 3 × 3 × 3

63 = 3 × 3 × 7

HCF = 3 × 3 = 9

Therefore, the HCF of 27, 63 is 9

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 9

36 = 2 × 2 × 3 × 3

84 = 2 × 2 × 3 × 7

HCF = 2 × 2 × 3 = 12

Therefore, the HCF of 36, 84 is 12

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 11

34 = 2 × 17

102 = 2 × 3 × 17

HCF = 2 × 17 = 34

Therefore, the HCF of 34, 102 is 34

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 13

70 = 2 × 5 × 7

105 = 3 × 5 × 7

175 = 5 × 5 × 7

HCF = 5 × 7 = 35

Therefore, the HCF of 70, 105, 175 is 35

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 16

91 = 7 × 13

112 = 2 × 2 × 2 × 2 × 7

Therefore, the HCF of 91, 112, 49 is 7

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 -19

54 = 2 × 3 × 3 × 3

81 = 3 × 3 × 3 × 3

Therefore, the HCF of 18, 54, 81 is 9

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 22

12 = 2 × 2 × 3

45 = 3 × 3 × 5

75 = 3 × 5 × 5

Therefore, the HCF of 12, 45, 75 is 3

2. What is the HCF of two consecutive

(a) numbers?

(b) even numbers?

(a) The HCF of two consecutive numbers is 1

Example: The HCF of 2 and 3 is 1

(b) The HCF of two consecutive even numbers is 2

Example: The HCF of 2 and 4 is 2

Example: The HCF of 3 and 5 is 1

3. HCF of co-prime numbers 4 and 15 was found as follows by factorisation:

4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

No. The answer is not correct. The correct answer is 1.

Access Other Exercise Solutions of Class 6 Maths Chapter 3: Playing with Numbers

Exercise 3.1 Solutions

Exercise 3.2 Solutions

Exercise 3.3 Solutions

Exercise 3.4 Solutions

Exercise 3.5 Solutions

Exercise 3.7 Solutions

Also, explore –

NCERT Solutions for Class 6 Maths Chapter 3

NCERT Solutions for Class 6

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NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. It helps the students to understand slowly and to get practice well to become perfect and again a good score in their examination.

These materials are prepared based on Class 6 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 6 Solutions Maths Chapter 3 Playing With Numbers are in accordance with the latest CBSE guidelines and marking schemes

Class 6 Maths Chapter 3 Exercise 3.1 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.1 00001

Class 6 Maths Chapter 3 Exercise 3.2 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.2 00001

Class 6 Maths Chapter 3 Exercise 3.3 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.3 00001

Class 6 Maths Chapter 3 Exercise 3.4 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.4 00001

Class 6 Maths Chapter 3 Exercise 3.5 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.5 00001

Class 6 Maths Chapter 3 Exercise 3.6 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.6 00001

Class 6 Maths Chapter 3 Exercise 3.7 Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.7 00001

Important Questions for CBSE Class 6 Maths Chapter 3 – Playing with Numbers

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Maths is one of the important subjects taught in school. We require Maths in our daily life to develop the power of analytical skills, reasoning and we begin with mathematical abilities to deal with numbers in lower classes.

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Chapter 3 of Class 6 Maths is about playing with numbers. It includes prime and composite numbers, divisibility, factors and multiples. It also includes two vital concepts- Highest Common Factor (HCF) and Lowest Common Multiple (LCM). The chapter is quite lengthy and has different questions, and students must practise questions from this chapter to clear their concepts.

Extramarks is a leading educational company that helps students by providing different study materials. Extramarks subject experts identify the importance of practising questions regularly. For this purpose, they have prepared the Important Questions Class 6 Maths Chapter 3. They have collected several important questions and provided the solutions in the question series. You may follow this article to solve different types of questions.

Extramarks, one of the leading educational platforms, believes in incorporating the best learning experiences through its own repository.To enjoy the maximum benefit of these resources,one may register on the official website of Extramarks and download a wide range of study materials. We provide CBSE syllabus, NCERT books, CBSE past years’ question papers , CBSE extra questions , CBSE sample papers, CBSE revision notes , NCERT solutions, NCERT important questions and much more.

Get Access to CBSE Class 6 Maths Important Questions with Solutions

Also, get access to CBSE Class 6 Maths Important Questions for other chapters too:

Playing with Numbers Class 6 Extra Questions With Answers

As stated above,Extramarks faculty experts have collected the questions from different sources like the textbook exercise, NCERT exemplar and reference books. They have taken help from CBSE past years’ question papers and CBSE sample question papers. They have provided the answers to the questions. Thus, students will find questions and solutions in the Important Questions Class 6 Maths Chapter 3 article extremely beneficial. The following are some of the important questions – to get an overview of the questions and for further practice one may sign up at Extramarks website.

Question 1. Write down all the factors of the following numbers given below:

24 = 1 × 24

Stop here as factors of 4 and 6 have already been counted. .

Therefore, the factors of 24 are – 1,2,3,4,6,8,12 and 24

15 = 1 × 15

Stop here, as factors of 3 and 5 have already been counted.

Therefore, the factors of 15 are – 1, 3, 5 and 15

21 = 1 × 21

Stop here, as factors 3 and 7 have occurred earlier.

Therefore, the factors of 21 are – 1, 3, 7 and 21

27 = 1 × 27

Stop here, as 3 and 9 have occurred earlier.

Therefore, the factors of 27 are – 1, 3, 9 and 27

12 = 1 × 12

Stop here, as the factors of 3 and 4 have already occurred earlier.

Therefore, the factors of 12 are – 1, 2, 3, 4, 6 and 12

20 = 1 × 20

20 = 2 × 10

Stop here as the factors of 4 and 5 have occurred earlier.

Therefore, the factors of 20 are – 1, 2, 4, 5, 10 and 20

18 = 1 × 18

Stop here, as 3 and 6 have already occurred earlier.

Therefore, the factors of 18 are – 1, 2, 3, 6, 9 and 18

23 = 1 × 23

23 = 23 × 1

As 1 and 23 have occurred earlier

Therefore, the factors of 23 are – 1 and 23

36 = 1 × 36

36 = 2 × 18

36 = 3 × 12

Stop here since both factors (6) are the same. Therefore, the factors of 36 are – 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Question 2. Write the first five multiples of:

(i) The required five multiples are –

Therefore, the first five multiples of 5 are 5, 10, 15, 20 and 25.

(ii) The required multiples are:

Therefore, the first five multiples of 8 are 8, 16, 24, 32 and 40.

(iii) The required multiples are:

Therefore, the first five multiples of 9 are 9, 18, 27, 36 and 45.

Question 3. State whether the following statements are True(T) or False(F) –

(i) The total sum of three odd numbers is even.

(ii) The total sum of two odd numbers and one even number is even.

(iii) The product of 3 odd numbers is odd.

(iv) If an even number is divided by two, the quotient is always odd.

(v) All prime numbers are odd.

(vi) Prime numbers don’t have any factors.

(vii) The sum of two prime numbers is always even.

(viii) Two is the only even prime number.

(ix) All the even numbers are composite numbers.

(x) The product of 2 even numbers is always even.

(i) False. The sum of 3 odd numbers is odd.

For example: 7 + 9 + 5 = 21 i.e odd number

(ii) True. The sum of 2 odd numbers and 1 even number is even.

For example: 3 + 5 + 8 = 16 i.e is an even number.

(iii) True. The product of 3 odd numbers is odd.

For example: 3 × 7 × 9 = 189 i.e is an odd number.

(iv) False. If an even number is divided by two, the quotient is even.

For example: 8 ÷ 2 = 4

(v) False, All the prime numbers are not odd.

Example: Two is a prime number, but it is also an even number.

(vi) False. Since one and the number itself are factors of the number

(vii) False. The sum of 2 prime numbers may also be an odd number

For example: 2 + 5 = 7 which is an odd number.

(viii) True. 2 is the only even and the lowest prime number.

(ix) False. Since 2 is a prime number but not a composite number.

(x) True. The product of 2 even numbers is always even.

For example: 2 × 4 = 8 which is an even number.

Question 4. The numbers 13 and 31 both are prime numbers. Both of these numbers have the same digits, one and three. Find such pairs of all the prime numbers up to 100.

The prime number pairs with the same digits up to 100 are as follows:

(a) 17 and 71

(b) 37 and 73

Question 5. Write down separately the prime and composite numbers which are less than 20.

2,3,5,7,11,13,17 and 19 are the prime numbers less than 20

4,6,8,9,10,12,14,15,16 and 18 are the composite numbers less than 20

Question 6. What is the greatest prime number between 1 and 10?

2,3,5 and 7 are the prime numbers between 1 and 10. 7 is the greatest prime number among them.

Question 7. Express the following given numbers as the sum of two odd primes.

(i) 3 + 41 = 44

(ii) 5 + 31 = 36

(iii) 5 + 19 = 24

(iv) 5 + 13 = 18

Question 8. Which of the following numbers is prime?

1 × 23 = 23

23 × 1 = 23

Therefore, 23 has only 2 factors, that is, 1 and 23. Hence, it is a prime number.

1 × 51 = 51

3 × 17 = 51

Therefore 51 has 4 factors that are 1, 3, 17 and 51. So, it is not a prime number, and it is a composite number.

1 × 37 = 37

37 × 1 = 37

Therefore 37 has 2 factors, 1 and 37. Hence, it is a prime number.

1 × 26 = 26

2 × 13 = 26

Therefore 26 has 4 factors 1, 2, 13 and 26. So, it is not a prime number, and it is a composite number.

Question 9. Express each of the following given numbers as the sum of 3 odd primes:

(i) 3 + 5 + 13 = 21

(ii) 3 + 5 + 23 = 31

(iii) 13 + 17 + 23= 53

(iv) 7 + 13 + 41 = 61

Question 10. Write 5 pairs of prime numbers less than 20 whose sum is divisible by five. (Hint: 3 + 7 = 10)

The 5 pairs of prime numbers less than 20 whose sum is divisible by 5 are

(i) 2 + 3 = 5

(ii) 2 + 13 = 15

(iii) 3 + 17 = 20

(iv) 7 + 13 = 20

(v) 19 + 11 = 30

Question 11. Fill in the blanks:

(i) A number with only two factors is called a ______.

(ii) A number with more than two factors is called a ______.

(iii) 1 is neither ______ nor ______.

(iv) The smallest prime number is ______.

(v) The smallest composite number is _____.

(vi) The smallest even number is ______.

(i) A number with only two factors is called a prime number.

(ii) A number with more than two factors is called a composite number.

(iii) 1 is neither a prime number nor a composite number.

(iv) The smallest prime number is 2

(v) The smallest composite number is 4

(vi) The smallest even number is 2.

Question 12. By using divisibility tests, determine which of the following given numbers are divisible by 6:

(vi) 438750

(vii) 1790184

(viii) 12583

(ix) 639210

As the last digit of the number is four. Therefore, the number is divisible by two.

By adding up all the digits of the number, we get 27 which is divisible by three. Hence, the number is divisible by 3

∴ The number is divisible by both two and three. Hence, the number is divisible by 6

As the last digit of the number is eight. Hence, the number is divisible by two.

By adding up all the digits of the number, we get 16 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by both two and three. Therefore, the number is not divisible by six.

Since the last digit of the number is five, which is not divisible by two. Hence, the number is not divisible by two.

By adding all the digits of the number, we get 15 divisible by three. Therefore, the number is divisible by three.

∴ The number is not divisible by two. . Hence, the number is not divisible by six.

As the last digit of the number is three, which is not divisible by two. Hence, the number is not divisible by two.

By adding up all the digits of the number, we get 15 divisible by three. Hence, the number is divisible by three.

∴ The number is not divisible by two.. Hence, the number is not divisible by six.

As the last digit of the number is two. Hence, the number is divisible by two.

The sum of all the digits of the number, we get 20 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by three. Hence, the number is not divisible by six.

As the last digit of the number is zero. Hence, the number is divisible by two.

By adding up all the digits of the number, we get 27 which is divisible by three. Hence, the number is divisible by three.

∴ The number is divisible by both two and three. Hence, the number is divisible by six.

As the last digit of the number is four. Hence, the number is divisible by two.

By adding up all the digits of the number, we get 30 divisible by 3. Hence, the number is divisible by 3

As the last digit of the number is three. Hence, the number is not divisible by two

By adding all the digits of the number, we get 19 which is not divisible by three. Hence, the number is not divisible by three.

∴ The number is not divisible by both two and three. Hence, the number is not divisible by six

By adding up all the digits of the number, we get 21 which is divisible by three. Hence, the number is divisible by three

By summing up all the digits of the number, we get 23 which is not divisible by three. Hence, the number is not divisible by three.

Question 13. Find the common factors of:

(i) 20 and 28

(ii) 15 and 25

(iii) 35 and 50

(iv) 56 and 120

1, 2, 4, 5, 10 and 20 are factors of 20

1, 2, 4, 7, 14 and 28 are factors of 28

Common factors = 1, 2, 4

1, 3, 5 and 15 are the factors of 15

1, 5 and 25 are the factors of 25

Common factors = 1, 5

1,5,7 and 35 are the factors of 35

1, 2, 5, 10, 25 and 50 are the factors of 50

1,2,4,7,8,14,28 and 56 are the factors of 56

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60 and 120 are factors of 120

Common factors = 1, 2, 4, 8

Question 14. Using divisibility tests, determine which of the following given numbers are divisible by 11:

(iii) 7138965

(iv) 70169308

(v) 10000001

(vi) 901153

Sum of digits at odd places = 5 + 4

Sum of digits at even places = 4 + 5

Difference between odd place and even place= 9 – 9 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is zero. Hence, 5445 is divisible by 11

Sum of digits at the odd places = 4 + 8 + 1

Sum of digits at the even places = 2 + 0

Difference = 13 – 2 = 11

As the difference between the sum of digits at odd places and the sum of digits at even places is 11, which is divisible by 11. Hence, 10824 is divisible by 11

Sum of digits at the odd places = 5 + 9 + 3 + 7 = 24

Sum of digits at the even places = 6 + 8 + 1 = 15

Difference = 24 – 15 = 9

As, the difference between the sum of digits at odd places and the sum of digits at even places is nine, which is not divisible by 11. Hence, 7138965 is not divisible by 11

Sum of digits at the odd places = 8 + 3 + 6 + 0

Sum of digits at the even places = 0 + 9 + 1 + 7

Difference = 17 – 17 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is 0. Hence, 70169308 is divisible by 11

Sum of digits at odd places = 1

Sum of digits at even places = 1

Difference = 1 – 1 = 0

As the difference between the sum of digits at odd places and the sum of digits at even places is 0. Hence, 10000001 is divisible by 11

Sum of digits at the odd places = 3 + 1 + 0

Sum of digits at the even places = 5 + 1 + 9

Difference = 15 – 4 = 11

As, the difference between the sum of digits at odd places and the sum of digits at even places is 11, which is divisible by 11. Hence, 901153 is divisible by 11.

Question 15. Which of the following statements is true?

(i) If the number is divisible by 3, it must be divisible by 9.

(ii) If the number is divisible by 9, it must be divisible by 3.

(iii) A number is divisible by 18 if it is divisible by both 3 and 6.

(iv) If a number is divisible by 9 and 10, then it must be divisible by 90.

(v) If two numbers are co-primes, at least one of them must be prime.

(vi) All numbers divisible by four must also be divisible by 8.

(vii) All numbers divisible by eight must also be divisible by 4.

(viii) If a number exactly divides two numbers separately, it must exactly divide their sum.

(ix) If a number exactly divides the sum of two numbers, it must divide the two numbers separately.

(i) False, six is divisible by three but is not divisible by 9

(ii) True, as 9 = 3 × 3. Therefore, if a number is divisible by nine, it will also be divisible by 3

(iii) False. Since 30 is divisible by both three and six but is not divisible by 18.

(iv) True, as 9 × 10 = 90. Therefore, if the number is divisible by both nine and ten, then it is divisible by 90

(v) False, because 15 and 32 are co-primes and also composite numbers.

(vi) False, as 12 is divisible by four but is not divisible by 8

(vii) True, as 2 × 4 = 8. Therefore, if a number is divisible by eight, it will also be divisible by 2 and 4.

(viii) True, as 2 divides 4 and 8 and it also divides 12 (4 + 8 = 12)

(ix) False, since 2 divides 12, but it does not divide 7 and 5

Benefits of Solving Class 6 Maths Chapter 3 Extra Questions

Extramarks believes in incorporating the best learning experiences through its own repository.To enjoy the maximum benefit of these resources , students just need to register themselves at Extramarks official website and stay ahead of the competition. Practice is a key to getting better in Maths. Students must solve questions as much as possible to clear their concepts. The experts identify the importance of practice. For this purpose, they have made the Important Questions Class 6 Maths Chapter 3 to help students. They have collected the questions from various sources and provided the answers too. Experienced professionals have further checked the solutions to ensure the best content for students. Thus, students will have multiple benefits if they follow the Important Questions Class 6 Maths Chapter 3. The benefits are-

The textbook exercise is often not enough for students. So, they must take help from other references. The experts have collected questions from different sources so that students need not search for similar study materials for further practice elsewhere. Apart from the textbook, they have taken help from CBSE sample papers and CBSE past years’ question papers. Thus, students have a complete set of practice study materials at their disposal not just for Maths but for other subjects as well. Students will find one of them in the class 6 playing with numbers extra questions . So, it will help students in revising and practising to get a 100% score in Maths.
Only solving questions may not be enough to score better in exams. Students must check the answers and get feedback. Sometimes, there can be errors in their processes of solving a problem. Keeping this fact in mind, the experts have also solved the questions and provided detailed solutions with step by step explanation. Experienced professionals have further checked the answers to ensure the answers are foolproof. . Thus, students will find the questions and the solutions in the Important Questions Class 6 Maths Chapter 3.
The experts have tried to include every kind of question that is usually expected in exams from the chapter. They have also included questions from past years’ question papers to provide an idea of possible types of questions in exams. Apart from this, they have given the answers in the Chapter 3 Class 6 Maths Important Questions so that students check the answers and solve their doubts. Thus, if students follow the question series, it will increase their confidence, strengthen their knowledge of maths and help them in their performance.

Extramarks subject experts understand the importance of solving important questions and we take our role seriously to provide the best resource to the students and help them excel in academics We provide a large variety of study materials. Like the Maths Class 6 Chapter 3 Important Questions, you will find important questions from other chapters of Maths Class 6. Register on the official website of Extramarks to access a wide range of materials like the CBSE syllabus , NCERT books, CBSE sample papers, CBSE past years’ question papers, NCERT exemplar, NCERT solutions, vital formulas and much more. The links to the following study materials are given below –

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Q.1 A greatest 3 ?digit number exactly divisible by 8, 10 and 14 is:

The prime factors of 8 = 2 × 2 × 2

The prime factors of 10 = 2 × 5

The prime factors of 14 = 2 × 7

LCM of 8, 10 and 14 = 2 × 2 × 2 × 5 × 7

The greatest number of 3 digits is 999.

999/280 gives, quotient = 3, remainder = 159

Therefore, the greatest 3-digit number exactly divisible by 8, 10 and 12 = 999 ? 159 = 840.

Q.2 Rajesh bought two barrels of oil of capacities 75 litres and 69 litres. The maximum capacity of a container, which can measure the oil in exact number of times, is

The prime factors of 75 = 3 × 5 × 5

The prime factors of 69 = 3 × 23

HCF of 75 and 69 is 3.

Therefore, the maximum capacity of a container used to measure the oil in exact number of times is 3 litres.

Q.3 Which of the following are co-prime numbers?

The common factor of 7 and 14 is 7, so these are not co-primes.

The common factor of 8 and 24 is 8, so these are not co-primes.

The common factor of 15 and 21 is 3, so these are not co-primes.

The common factor of 7 and 15 is 1, so these are co-primes.

Q.4 What is the HCF of two prime numbers?

The HCF of two prime numbers is 1.

Q.5 Find the prime factorisation of 96.

2 96 2 48 2 24 2 12 2 6 2 3 1

Prime factorisation of 96 is 2 — 2 — 2 — 2 — 2 — 3

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Cbse important questions for class 6 maths, chapter 1 - knowing our numbers.

Chapter 2 - Whole Numbers

Chapter 4 - basic geometrical ideas, chapter 5 - understanding elementary shapes, chapter 6 - integers, chapter 7 - fractions, chapter 8 - decimals, chapter 9 - data handling, chapter 10 - mensuration, chapter 11 - algebra, chapter 12 - ratio and proportion, chapter 13 - symmetry, chapter 14 - practical geometry, faqs (frequently asked questions), 1. what does class 6 maths chapter 3 contain.

Chapter 3 of Class 6 Maths is about the relationship between numbers. It deals with prime and compound numbers, divisibility, factors and multiples etc. It contains two main concepts- Highest Common Factor or HCF and Lowest Common Multiple or LCM. Students must practise questions from this chapter as a wide range of questions can be made from the chapter. You can follow the Important Questions Class 6 Maths Chapter 3 compiled by our experts. Apart from questions, you will also find solutions. So, it will greatly help you in preparing for exams.

2. Is Class 6 Maths Chapter 3 tough?

Students may find this chapter a bit difficult because it is lengthy and contains different concepts. One can take help from the Important Questions Class 6 Maths Chapter 3 to clear the concepts. Ideas like HCF and LCM may be a new concept for the students. So, they must practise questions to get conceptual clarity. . But the chapter is not complex; students can easily understand the subject matter if they sincerely follow the textbook and practice regularly.

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Assertion and Reason Questions Class 6 Maths Chapter 3 Playing with Numbers

Hello Students are looking for Assertion Reason Questions Class 6 Maths Chapter 3 Playing with Numbers, If yes here we Net Explanations have given Assertion and Reason MCQ for 6th Class Maths Chapter 3.

Solved CBSE Class 6 Maths Chapter 3 Assertion Reasoning Questions – Playing with Numbers. Here we (Net Explanations) working very hard to providing you with the Important Assertion Reason Questions for this Chapter.

1.) Assertion (A) – T he factors of 34 are 1, 2, 17 and 34 itself

Reason (R) – every factor is less than or equal to the given number.

a) Both A and R are true and R is the correct explanation of A

b) Both A and R are true but R is not the correct explanation of A

c) A is true but R is false

d) A is false but R is true

2.) Assertion (A) –The factors of 8 are 1, 2, 4, 8.

Reason (R) – every factor of a number is an exact divisor of that number.

3.) Assertion (A) –The factors of16 are 1, 2, 4, 8.

4.) Assertion (A) –The number 76 has 5 factors.

Reason (R) – number of factors of a given number are finite.

5.) Assertion (A) –The multiples of 7 are 7, 14, 21, 28,…

Reason (R) – every multiple of a number is greater than or equal to that number

6.) Assertion (A) –The multiples of 5 are 5, 10, 15, 20, …

Reason (R) – the number of multiples of a given number is infinite

7.) Assertion (A) –7 is a multiple of itself

Reason (R) – every number is a multiple of itself

8.) Assertion (A) –The sum of the factors of any number is twice the number.

Reason (R) – A number for which sum of all its factors is equal to twice the number is called a perfect number

9.) Assertion (A) –2 is a prime number.

Reason (R) – The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers

10.) Assertion (A) – 0 is a prime number

11.) Assertion (A) – 11 is a prime number

12.) Assertion (A) – 5 is a composite number.

Reason (R) – Numbers having more than two factors are called Composite numbers

13.) Assertion (A) –17 is a composite number.

14.) Assertion (A) – Prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.

15.) Assertion (A) –2, 4, 6, 8, 10, 12, 14 are odd numbers.

Reason (R) – Odd numbers cannot be divisible by 2.

16.) Assertion (A) – 2, 4, 6, 8, 10, 12, 14 are even numbers

Reason (R) – Even numbers should be divisible by 2.

17.) Assertion (A) –The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3.

18.) Assertion (A) – 55 is divisible by 10.

Reason (R) – if a number has 0 in the ones place then it is divisible by 10.

19.) Assertion (A) –525 is not divisible by 5.

Reason (R) – a number which has either 0 or 5 in its ones place is divisible by 5

20.) Assertion (A) – 4829 is divisible by 2.

Reason (R) – a number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.

21.) Assertion (A) – 479 is divisible by 3

Reason (R) –if the sum of the digits is a multiple of 3, then the number is divisible by 3.

22.) Assertion (A) – 572 is divisible by 4.

Reason (R) –a number with 3 or more digits is divisible by 3 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

23.) Assertion (A) – 48 is divisible by 8

Reason (R) –a number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8

24.) Assertion (A) – 36 is divisible by 9

Reason (R) –if the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

25.) Assertion (A) – 132 is divisible by 11.

Reason (R) –find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

26.) Assertion (A) – 3 is a factor of 18

Reason (R) –if a number is divisible by another number then it is divisible by each of the factors of that number

27.) Assertion (A) –60 is not divisible by 3 and 5 which are co-primes

Reason (R) –If a number is divisible by two co-prime numbers then it is divisible by their product also

28.) Assertion (A) –The HCF of 20, 28 and 36 is 2

Reason (R) –The Highest Common Factor(HCF) of two or more givennumbers is the highest (orgreatest) of their common factors

29.Assertion (A) – LCM of 12 and 18 is 36

Reason (R) –The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples

30.) Assertion (A) – The LCM of 20, 25 and 30 is 20

1: A 2:A 3:D 4:A 5:A 6:B

7:A 8:A 9:A 10:D 11:A 12:D

13:D 14:A 15:D 16:A 17:B 18:D

19:A 20:D 21:D 22:C 23:A 24:C

25:A 26:A 27:D 28:D 29:A 30:D

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Really very helpful for both kids and parents

Can u please explain question 6 . How can it be B it should be A know because it is the proper explanation for that.

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Class 6 Maths Chapter 3 Playing with numbers Worsheet

Table of Contents

Infinity Learn academic team have designed worksheet and questions for Chapter Playing with Numbers specifically for students of Class 6. Attentively framed questions give practice of all type of numerical which are further solved on step-by-step basis. Get Worksheet for Class 6 Maths Chapter Playing with Numbers and its solution is also referred. Students are recommended to first go through chapter theory and questions from textbook before attempting Infinity Learn worksheet.

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Worksheet On Playing With Numbers for Class 6 With Solutions

Q. What is the smallest prime number?

Answer: C) 2

Q. Which of the following numbers is divisible by 2?

Answer: B) 42

Q. Which is the smallest composite number?

Answer: C) 4

Q. What is the sum of the first 5 prime numbers?

Answer: D) 28

Q. Which of the following numbers is a perfect square?

Answer: B) 36

Q. What is the largest prime factor of 36?

Answer: B) 3

Q. What is the product of the first 3 prime numbers?

Answer: B) 6

Q. Which of the following numbers is divisible by both 2 and 3?

Answer: A) 18

Q. What is the smallest composite number greater than 10?

Answer: B) 12

Q. What is the sum of the first 5 composite numbers?

Answer: D) 40

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Q. What is the product of any two consecutive numbers?

A) Prime number

B) Odd number

C) Even number

D) Always divisible by 3

Answer: C) Even number

Q. Which of the following numbers is not divisible by 5?

Answer: A) 45

Q. What is the sum of any two consecutive odd numbers?

B) Even number

C) Odd number

Answer: B) Even number

Q. What is the smallest multiple of 7?

Answer: A) 7

Q. Which of the following is a prime number?

Answer: B) 41

Q. What is the sum of the digits of the number 123?

Q. Which of the following numbers is a multiple of 9?

Answer: A) 72

Q. What is the next prime number after 47?

Answer: D) 53

Q. Which of the following numbers is a perfect cube?

Answer: B) 81

Q. What is the sum of the first 5 odd numbers?

Answer: C) 35

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Unit 3: Playing with numbers

Playing with numbers 3.2

Playing with numbers 3.3

Playing with numbers 3.4

Playing with numbers 3.5

Playing with numbers 3.6

Playing with numbers 3.7

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Important Questions for CBSE Class 6 Maths Chapter 3 – Playing with Numbers

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Playing with Numbers Class 6 Extra Questions With Answers

Question 1. Write down all the factors of the following numbers given below:

Question 2. Write the first five multiples of:

Question 3. State whether the following statements are True(T) or False(F) –

Question 4. The numbers 13 and 31 both are prime numbers. Both of these numbers have the same digits, one and three. Find such pairs of all the prime numbers up to 100.

Question 5. Write down separately the prime and composite numbers which are less than 20.

Question 8. Which of the following numbers is prime?

Question 9. Express each of the following given numbers as the sum of 3 odd primes:

Question 10. Write 5 pairs of prime numbers less than 20 whose sum is divisible by five. (Hint: 3 + 7 = 10)

Question 11. Fill in the blanks:

Question 12. By using divisibility tests, determine which of the following given numbers are divisible by 6:

Question 13. Find the common factors of:

Question 14. Using divisibility tests, determine which of the following given numbers are divisible by 11:

Question 15. Which of the following statements is true?

Benefits of Solving Class 6 Maths Chapter 3 Extra Questions

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Chapter 2 - Whole Numbers

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Class 6 Maths Chapter 3 Playing with numbers Worsheet

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