These NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers InText Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers InText Questions

NCERT In-text Question Page No. 48

Question 1.

Find the possible factors of 45, 30 and 36.

Answer:

The possible factor of

45 = 1,3,5,9,15,45

30 = 1,2,3,5,6,10,15,30

36 = 1,2,3,4,6,9,12,18,36

NCERT In-text Question Page No. 52

Question 1.

Observe that 2 × 3 + 1 = 7 is a prime number. Here, 1 has been added to a multiple of 2 to get a prime number. Can you find some more numbers of this type?

Answer:

We can have:

2 × 2 + 1 = 5, which is a prime number.

2 × 5 + 1 = 11, which is a prime number.

2 × 6 + 1 = 13, which is a prime number.

2 × 8 + 1 = 17, which is a prime number.

2 × 9 + 1 = 19, which is a prime number.

2 × 11 + 1 = 23, which is a prime number.

NCERT In-text Question Page No. 58

Question 1.

Find the common factors of

(a) 8,20

(b) 9,15

Answre:

(a) 8, 20

Since, 8 = 1 × 8

8 = 2 × 4

∴ All the factors of 20 are: 1, 2, 4 and 8 …(i)

Again, 20 = 1 × 20

20 = 2 × 10

20 = 4 × 5

∴ All the factors of 20 are: 1, 2, 4, 5, 10 and 20 …(ii)

From (i) and (ii), common factors of 8 and 20 are: 1, 2 and 4.

(b) 9,15

We have: 9 = 1 × 9

9 = 3 × 3

∴ All the factors of 9 are: 1, 3 and 9 …(i)

Again, 15 = 1 × 15

15 = 3 × 5

∴ All the factors of 15 are: 1, 3, 5 and 15 …(ii)

From (i) and (ii), common factors of 9 and 15 are: 1 and 3.

NCERT In-text Question Page No. 61

Question 1.

Write the prime factorisations of 16, 28, 38.

Answer:

(i) 16

We have:

∴ Prime factorisation of 16 = 2 × 2 × 2 × 2

(ii) 28

We have:

∴ Prime factorisation of 28 = 2 × 2 × 7

(iii) 38

We have:

∴ Prime factorisation of 38 = 2 × 19

NCERT In-text Question Page No. 63

Question 1.

Find the HCF of the following:

(i) 24 and 36

(ii) 15, 25 and 30

(iii) 8 and 12

(iv) 12,16 and 28

Answer:

(i) 24 and 36

∵ Factors of 24 are: 1, 2, 3, 4, 6, 12 and 24

Factors of 36 are: 1, 2, 3, 4, 6, 12, 18 and 36

∵ Common factors are: 1, 2, 3, 4, 6 and 12

Since, the highest of these common factors = 12

∴ HCF of 24 and 36 = 12

(ii) 15, 25 and 30

∵ Factors of 15 are: 1, 3, 5 and 15

Factors of 25 are: 1, 5 and 25

Factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30

∴ Common factors are: 1 and 5

Since, the highest common factors is 5,

HCF of 15, 25 and 30 = 5

(iii) 8 and 12

∵ Factors of 8 are: 1, 2, 4 and 8

Factors of 12 are: 1, 2, 3, 4, 6 and 12

∴ Common factors are: 1, 2, 4

Since, the highest common factors is 4,

∴ HCF of 8 and 12 = 4

(iv) 12,16 and 28

∵ Factors of 12 are: 1, 2, 3, 4, 6 and 12

Factors of 16 are: 1, 2, 4, 8 and 16

Factors of 28 are: 1, 2, 4, 7, 14 and 28

∴ Common factors are: 1, 2, 4

Since, the highest common factors is 4,

∴ HCF of 12, 16 and 28 = 4