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Class 6 Playing with Numbers NCERT Solutions

# Chapter 3: Playing with Numbers

## ExERCISE 3.1

Questions 1. Write all the factors of the following numbers:

(a) 24 (b) 15 (c) 21 (d) 27 (e) 12 (f) 20 (g) 18 (h) 23 (i) 36

Answer:

(a) 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 6 x 4

∴ Factors of 24 = 1, 2, 3, 4, 6, 12, 24

(b) 15 = 1 x 15 = 3 x 5 = 5 x 3

∴ Factors of 15 = 1, 3, 5, 15

(c) 21 = 1 x 21 = 3 x 7 = 7 x 3

∴ Factors of 21 = 1, 3, 7, 21

(d) 27 = 1 x 27 = 3 x 9 = 9 x 3

∴ Factors of 27 = 1, 3, 9, 27

(e) 12 = 1 x 12 = 2 x 6 = 3 x 4 = 4 x 3

∴ Factors of 12 = 1, 2, 3, 4, 6, 12

(f) 20 = 1 x 20 = 2 x 10 = 4 x 5 = 5 x 4

∴ Factors of 20 = 1, 2, 4, 5, 10, 20

(g) 18 = 1 x 18 = 2 x 9 = 3 x 6

∴ Factors of 18 = 1, 2, 3, 6, 9, 18

(h) 23 = 1 x 23

∴ Factors of 23 = 1, 23

(i) 36 = 1 x 36 = 2 x 18 = 3 x 12 = 4 x 9 = 6 x 6

∴ Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

2. Write first five multiples of:

(a) 5 (b) 8 (c) 9

Answer

(a) 5 x 1 = 5, 5 x 2 = 10, 5 x 3 = 15, 5 x 4 = 20, 5 x 5 = 25

∴ First five multiples of 5 are 5, 10, 15, 20, 25.

(b) 8 x 1 = 8, 8 x 2 = 16, 8 x 3 = 24, 8 x 4 = 32, 8 x 5 = 40

∴ First five multiples of 8 are 8, 16, 24, 32, 40.

(c) 9 x 1 = 9, 9 x 2 = 18, 9 x 3 = ,27, 9 x 4 = 36, 9 x 5 = 45

∴ First five multiples of 9 are 9, 18, 27, 36, 45.

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

Column 1 Column 2

(i) 35 (a) Multiple of 8

(ii) 15 (b) Multiple of 7

(iii) 16 (c) Multiple of 70

(iv) 20 (d) Factor of 30

(v) 20 (e) Factor of 50

Answers

3. (i) → (b), (ii) → (d), (iii) → (a), (iv) → (f), (v) → (e)

4. Find all the multiples of 9 up to 100.

Answers

Multiples of 9 up to 100 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

## EXERCISE. 3.2

1. What is the sum of any two:

(a) Odd numbers.

(b) Even numbers.

Answers:

1. (a) The sum of any two odd numbers is an even number.

Example: 1 + 3 = 4, 3 + 5 = 8

(b) The sum of any two even numbers is an even number.

Example: 2 + 4 = 6, 6 + 8 = 14

2. State whether the following statements are true or false:

(a) The sum of three odd numbers is even.

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

(c) The product of three odd numbers is odd.

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

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

Answers:

(a) False (b) True (c) True (d) False (e) False (f) False (g) False (h) True (i) False (j) True

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

Answers:

3. 17 and 71; 37 and 73; 79 and 97

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

Answers:

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19

Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

5. What is the greatest prime number between 1 and10?

Answers:

The greatest prime number between 1 and 10 is ‘7’

6. Express the following as the sum of two odd numbers:

(a) 44 (b) 36 (c) 24 (d) 18

Answers:

6. (a) 3 + 41 = 44 (b) 5 + 31 = 36 (c) 7 + 17 = 24 (d) 7 + 11 = 18

7. Give three pairs of prime numbers whose difference is 2.

[Remark: Two prime numbers whose difference is 2 are called twin primes.]

Answers:

3 and 5; 5 and 7; 11 and 13

8. Which of the following numbers are prime:

(a) 23 (b) 51 (c) 37 (d) 26

Answers:

(a) 23 and (c) 37 are prime numbers.

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

Answers:

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

10. Express each of the following numbers as the sum of three odd primes:

(a) 21 (b) 31 (c) 53 (d) 61

Answers:

(a) 21 = 3 + 7+ 11 (b) 31 = 3 + 11 + 17

(c) 53 = 13 + 17 + 23 (d) 61 = 19 + 29 + 13

11. Write five pairs of prime numbers less than 20 whose sum is divisible by5.

[Hint: 3 + 7 = 10]

Answers:

2 + 3= 5; 7 + 13 = 20; 3 + 17 = 20; 2 + 13 = 15; 5 + 5 = 10

12. Fill in the blanks:

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

(b) A number which has more than two factors is called a———— .

(c) 1 neither nor———– .

(d) The smallest prime number is———— .

(e) The smallest composite number is ——————_.

(f) The smallest even number is————- .

Answers:

(a) Prime number

(b) Composite number

(c) Prime number and composite number

(d) 2

(e) 4

(f) 2

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