CBSE Class 6 Mathematics Chapter 3: Playing With Numbers NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 3, Playing With Numbers, lays the groundwork for understanding number theory. This chapter guides students through identifying factors and multiples, distinguishing between prime and composite numbers, and applying divisibility rules. The NCERT Solutions offer clear, step-by-step explanations to help students master these concepts. For instance, finding factors involves listing all pairs of numbers that multiply to a specific number, while multiples are found through repeated addition or multiplication. These solutions are crafted to build a robust number sense, essential for future mathematical studies. They serve as a valuable tool for both exam preparation and reinforcing learning.

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BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3: Playing With Numbers

Chapter summary

Chapter 3, Playing With Numbers, for Class 6 Mathematics focuses on understanding the basic building blocks of numbers: factors and multiples. The NCERT Solutions cover exercises on finding all factors of given numbers, listing the first few multiples, matching numbers with their properties (like being a multiple or factor), and identifying multiples within a specific range. This chapter lays the groundwork for more advanced number theory concepts.

Learning outcomes

  • Understand the concept of factors and how to find them for any given number.
  • Identify and list the multiples of a given number.
  • Distinguish between factors and multiples.
  • Apply knowledge of factors and multiples to solve problems.
  • Recognize number patterns related to factors and multiples.

Topics covered

Paper topics

  • Factors
  • Multiples
  • Finding Factors
  • Finding Multiples
  • Number Properties
  • Divisibility
  • Number Theory Basics

Important topics

  • Understanding Factors
  • Listing Multiples
  • Identifying Factors and Multiples
  • Number Range Problems

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Questions and Solutions

Question 1

Write all the factors of the following numbers:
  1. 24
  2. 15
  3. 21
  4. 27
  5. 12
  6. 20
  7. 18
  8. 23
  9. 36
Solution:

To find all the factors of a number, we look for pairs of numbers that multiply together to give the original number. We start with 1 and the number itself, and then systematically check other numbers.

  1. Factors of 24: We can find pairs like 1 × 24, 2 × 12, 3 × 8, and 4 × 6. Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
  2. Factors of 15: The pairs are 1 × 15 and 3 × 5. Thus, the factors of 15 are 1, 3, 5, and 15.
  3. Factors of 21: The pairs are 1 × 21 and 3 × 7. So, the factors of 21 are 1, 3, 7, and 21.
  4. Factors of 27: The pairs are 1 × 27 and 3 × 9. The factors of 27 are 1, 3, 9, and 27.
  5. Factors of 12: The pairs are 1 × 12, 2 × 6, and 3 × 4. The factors of 12 are 1, 2, 3, 4, 6, and 12.
  6. Factors of 20: The pairs are 1 × 20, 2 × 10, and 4 × 5. The factors of 20 are 1, 2, 4, 5, 10, and 20.
  7. Factors of 18: The pairs are 1 × 18, 2 × 9, and 3 × 6. The factors of 18 are 1, 2, 3, 6, 9, and 18.
  8. Factors of 23: Since 23 is a prime number, its only factors are 1 and itself. The pair is 1 × 23. The factors of 23 are 1 and 23.
  9. Factors of 36: The pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Question 2

Write first five multiples of:
  1. 5
  2. 8
  3. 9
Solution:

To find the first five multiples of a number, we multiply the number by 1, 2, 3, 4, and 5.

  1. Multiples of 5:

    5 \times 1 = 5

    5 \times 2 = 10

    5 \times 3 = 15

    5 \times 4 = 20

    5 \times 5 = 25

    The first five multiples of 5 are 5, 10, 15, 20, and 25.
  2. Multiples of 8:

    8 \times 1 = 8

    8 \times 2 = 16

    8 \times 3 = 24

    8 \times 4 = 32

    8 \times 5 = 40

    The first five multiples of 8 are 8, 16, 24, 32, and 40.
  3. Multiples of 9:

    9 \times 1 = 9

    9 \times 2 = 18

    9 \times 3 = 27

    9 \times 4 = 36

    9 \times 5 = 45

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

Question 3

Match the items in column 1 with the items in column 2:

Column 1

  1. 35
  2. 15
  3. 16
  4. 20
  5. 25

Column 2

  1. Multiple of 8
  2. Multiple of 7
  3. Multiple of 70
  4. Factor of 30
  5. Factor of 50
Solution:

We need to check the relationship between each number in Column 1 and the descriptions in Column 2.

  • 35: Is it a multiple of 8? No. Is it a multiple of 7? Yes, 35 = 7 \times 5. Is it a multiple of 70? No. Is it a factor of 30? No. Is it a factor of 50? No. So, 35 matches with (b) Multiple of 7.
  • 15: Is it a multiple of 8? No. Is it a multiple of 7? No. Is it a multiple of 70? No. Is it a factor of 30? Yes, 30 = 15 \times 2. Is it a factor of 50? No. So, 15 matches with (d) Factor of 30.
  • 16: Is it a multiple of 8? Yes, 16 = 8 \times 2. Is it a multiple of 7? No. Is it a multiple of 70? No. Is it a factor of 30? No. Is it a factor of 50? No. So, 16 matches with (a) Multiple of 8.
  • 20: Is it a multiple of 8? No. Is it a multiple of 7? No. Is it a multiple of 70? No. Is it a factor of 30? No. Is it a factor of 50? No. (Note: The original source had a typo, listing 20 twice and missing a match. Assuming the intention was to match 20 with a property, and based on common exercises, it might be intended to match with a factor of a number like 40 or 20 itself. However, strictly following the provided options, none fit perfectly. If we consider the possibility of a typo in the question and assume one of the options was meant to be 'Factor of 40' or 'Multiple of 4/5/10', we could proceed. Given the provided answer key implies a match, and re-examining the source, it seems the original question might have intended a different set of options or numbers. However, if we must choose from the given, and acknowledging the ambiguity, let's re-evaluate. The provided answer key suggests (iv) -> (f). There is no (f) in the options. Let's assume there was a typo and the question meant to include a match for 20. If we look at the provided answer key's mapping: (i) -> (b), (ii) -> (d), (iii) -> (a), (iv) -> (f), (v) -> (e). This implies 20 should match with (f) and 25 with (e). Since (f) is missing, and 25 is a factor of 50 (50 = 25 \times 2), let's assume (v) 25 matches with (e) Factor of 50. This leaves (iv) 20 to match with a missing option (f). If we assume the question intended to ask for a factor of 40, then 20 would fit. Without option (f), we cannot definitively match 20. However, if we strictly follow the provided answer key's mapping and assume (f) was intended for 20, we proceed with the given matches.) Let's assume the intended match for 20 was a factor of 40 (not listed).
  • 25: Is it a multiple of 8? No. Is it a multiple of 7? No. Is it a multiple of 70? No. Is it a factor of 30? No. Is it a factor of 50? Yes, 50 = 25 \times 2. So, 25 matches with (e) Factor of 50.

The correct matches are: (i) → (b), (ii) → (d), (iii) → (a), (v) → (e). The match for (iv) 20 is unclear due to missing options or typos in the source.

Question 4

Find all the multiples of 9 up to 100.
Solution:

To find the multiples of 9 up to 100, we start multiplying 9 by consecutive natural numbers (1, 2, 3, ...) until the product exceeds 100.

9 \times 1 = 9

9 \times 2 = 18

9 \times 3 = 27

9 \times 4 = 36

9 \times 5 = 45

9 \times 6 = 54

9 \times 7 = 63

9 \times 8 = 72

9 \times 9 = 81

9 \times 10 = 90

9 \times 11 = 99

9 \times 12 = 108 (This is greater than 100, so we stop here).

Therefore, the multiples of 9 up to 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.

Common mistakes

  • Forgetting to include 1 and the number itself when listing factors.
  • Stopping the listing of multiples prematurely.
  • Confusing factors with multiples.
  • Missing some factor pairs when finding all factors.

Revision tips

  • Practice finding factors for a variety of numbers, including larger ones.
  • Use multiplication tables to quickly identify multiples.
  • Create your own matching exercises using factors and multiples.
  • Review the definitions of factor and multiple regularly.

Practice MCQs

Q1. Which of the following are factors of 36?

Q2. What are the first four multiples of 7?

Q3. Which number is a multiple of both 5 and 7?

Q4. Which of the following is a factor of 27?

Q5. What is the largest multiple of 9 that is less than 100?

Frequently asked questions

What is the main focus of Chapter 3, Playing With Numbers, for Class 6 Maths?

This chapter focuses on understanding the fundamental concepts of factors and multiples of numbers, and how to identify them.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the methods to find factors and multiples accurately.

What is a factor of a number?

A factor of a number is any number that divides it exactly, without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

What are multiples of a number?

Multiples of a number are obtained by multiplying it with consecutive natural numbers (1, 2, 3, and so on). For example, the first five multiples of 5 are 5, 10, 15, 20, and 25.

Are there any specific techniques taught for finding factors?

Yes, the solutions demonstrate finding factors by systematically checking pairs of numbers that multiply to the given number, ensuring all factors are identified.

Important links

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