SOLUTIONS FOR CBSE CLASS 6 NCERT MATHS CHAPTER 3 PLAYING WITH NUMBERS

Find here, the step-by-step and precisely written Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.1 and Exercise 3.2.

Solutions for CBSE class 6 NCERT Maths Chapter 3 deals with Factors and Multiple of Numbers. Factors and Multiples are very important concepts of number system. Whether classification of numbers, Comparison of numbers or Simplification, they have wide application in mathematics.

Before viewing the Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers, it is advised to go through the following topics –
• Factors and Multiples and
• HCF and LCM.

☆☆ Statements besides ℹ button are only for explanation and not a part of the answer.
☆☆ Question besides ❔ buttons are not from the NCERT textbooks.


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

Problems in Class 6 Exercise 3.1 require the knowledge of finding Factors and Multiples of Natural Numbers.

Number of factors for a number are finite but number of multiples are infinite.

EXERCISE 3.1
Factors | Multiples

QUESTION 1

Write all the factors of the following numbers

(i) 24 (ii) 15 (iii) 21

(iv) 27 (v) 12 (vi) 20

(vii) 18 (viii) 23 (ix) 36

ANSWER

(i) 1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24

All the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

(ii) 1 × 15 = 15
3 × 5 = 15

All the factors of 24 are 1, 3, 5 and 15.

(iii) 1 × 21 = 21
3 × 7 = 21

All the factors of 24 are 1, 3, 7 and 21.

(iv) 1 × 27 = 27
3 × 9 = 27

All the factors of 24 are 1, 3, 9 and 27.

(v) 1 × 12 = 12
2 × 6 = 12
3 × 4 = 12

All the factors of 24 are 1, 2, 3, 4, 6, and 12.

(vi) 1 × 20 = 20
2 × 10 = 20
4 × 5 = 20

All the factors of 24 are 1, 2, 4, 5, 10 and 20.

(vii) 1 × 18 = 18
2 × 9 = 18
3 × 6 = 18

All the factors of 24 are 1, 2, 3, 6, 9 and 18.

(viii) 1 × 23 = 23

All the factors of 24 are and 23.

(ix) 1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36

All the factors of 24 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.


❔ How factors of a number are found?

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.1 ]


QUESTION 2

Write first five multiples of
(i) 5 (ii) 8 (iii) 9

ANSWER

(i) 5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
5 × 5 = 25

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

(ii) 8 × 1 = 8
8 × 2 = 16
8 × 3 = 24
8 × 4 = 32
8 × 5 = 40

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

(iii) 9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45

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


❔ How to find multiples of a number?
❔ What is the difference between factors and multiples of a number?

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.1 ]


QUESTION 3

Match the items in column I with the items in column II

Column I
(i) 35
(ii) 15
(iii) 16
(iv) 20
(v) 25
Column II
(a) Multiple of 8
(b) Multiple of 7
(c) Multiple of 70
(d) Factor of 30
(e) Factor of 50
(f) Factor of 20

ANSWER

(i) – b
(ii) – d
(iii) – a
(iv) – f
(v) – e

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.1 ]

QUESTION 4

Find all the multiples of 9 upto 100.

ANSWER

9 × 1 = 9
9 × 2 = 18
9 × 3 = 27
9 × 4 = 36
9 × 5 = 45
9 × 6 = 54
9 × 7 = 63
9 × 8 = 72
9 × 9 = 81
9 × 10 = 90
9 × 11 = 99
9 × 12 = 108 > 100

Thus, Multiples of 9 upto 100 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 and 99.


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

Problems in Class 6 Exercise 3.2 require the knowledge of classifying Natural Numbers according to their Factors and Multiples.

Prime Numbers have only two factors, 1 and itself.

Composite Numbers have more than two factors.

Multiples of 2 are called Even numbers.

EXERCISE 3.2
Prime and Composite Numbers
Even and Odd Numbers

QUESTION 1

What is the sum of any two
(i) odd numbers (ii) even numbers

ANSWER

(i) Sum of any two odd numbers is always an even number. e.g., 3 + 5 = 8, 11 + 13 = 24.

(ii) Sum of any two even numbers is always an even number. e.g., 2 + 4 = 6, 8 + 12 = 20.


❔ What is the difference between an even and an odd number.

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]


QUESTION 2

True or False

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

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

(iii) The product of three odd numbers is odd.
– True

(iv) If an even number is divided by 2, the quotient is always odd.
– False

(v) All prime numbers are odd.
– False

(vi) Prime numbers do not have any factors.
– False

(vii) Sum of two prime numbers is always even.
– False

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

(ix) All even numbers are composite number.
– False

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


❔ What is a prime number?
❔ Which is the only prime number that is not odd?
❔ What is a composite number?
❔ Which is the only even natural number that is not composite?
❔ Which natural number is not prime not composite?
❔ Why 0 is not a prime number?
❔ Why 0 is not a composite number?

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]


QUESTION 3

The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.

ANSWER

17 and 71,
37 and 73,
79 and 97.

QUESTION 4

Write down separately the prime and composite numbers less than 20.

ANSWER

Prime numbers less than 20 are –
2, 3, 5, 7, 11, 13, 17 and 19

Composite numbers less than 20 are –
4, 6, 8, 9, 10, 12, 14, 15, 16 and 18.

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]

QUESTION 5

What is the greatest prime number between 1 and 10?

ANSWER

Prime numbers between 1 and 10 are –
2 < 3 < 5 < 7
Thus, greatest prime number between 1 and 10 is 7.

QUESTION 6

Express the following as the sum of two odd numbers
(i) 44 (ii) 36 (iii) 24 (iv) 18

ANSWER

(i) 44 = 21 + 23
(ii) 36 = 9 + 27
(iii) 24 = 11 + 13
(iv) 18 = 3 + 15.

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]

QUESTION 7

Give three pairs of prime numbers whose difference is two.

ANSWER

3 and 5,
5 and 7;
11 and 13


❔ What are co-primes?
❔ What are twin primes?

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]


QUESTION 8

Which of the following numbers are prime:
(i) 23 (ii) 51 (iii) 37 (iv) 26

ANSWER

(i) 23 and (iii) 37 are prime numbers.

QUESTION 9

Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

ANSWER

90, 91, 92, 93, 94, 95, 96

QUESTION 10

Express each of the following numbers as the sum of three odd primes
(i) 21 (ii) 31 (iii) 53 (iv) 61

ANSWER

(i) 21 = 3 + 7 + 11
(ii) 31 = 3 + 11 + 17
(iii) 53 = 13 + 17 + 23
(iv) 61 = 19 + 29 + 13.

[ Solutions for CBSE Class 6 NCERT Maths Chapter 3 Playing with Numbers | Exercise 3.2 ]

QUESTION 11

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

ANSWER

2 + 3 = 5
3 + 7 = 10
7 + 13 = 20
3 + 17 = 20
13 + 17 = 30

QUESTION 12

Fill in the blanks

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

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

(iii) 1 is neither composite nor prime .

(iv) The smallest prime number is 2 .

(v) The smallest composite number is 4 .

(vi) The smallest even number is 2 .

NCERT MATHS SOLUTION | CLASS 6 | CHAPTER 3 | PLAYING WITH NUMBERS

Exercise 3.1 | Exercise 3.2 | Exercise 3.3

Exercise 3.4 | Exercise 3.5 |

Exercise 3.6 | Exercise 3.7

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