Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers InText Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers InText Questions

Try These (Page 48)

Question 1.

Find the possible factors of 45, 30 and 36.

Solution:

(i) Factors of 45:

We have: 45 = 1 x 45

45 = 3 x 15

45 = 5 x 9

Factors of 45 are: 1, 3, 5, 9, 15 and 45.

(ii) Factors of 30:

30 = 1 x 30

30 = 2 x 15

30 = 3 x 10

30 = 5 x 6

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

(iii) Factors of 36:

36 = 1 x 36

36 = 2 x 18

36 = 3 x 12

36 = 4 x 9

36 = 6 x 6

Factors of 36 are: 1,2,3,4, 6,9, 12, 18 and 36.

Try These (Page 52)

Question 1.

Observe that 2 x 3 + 1 = 7 is a prime number Here,

I has been added to a multiple of 2 to get a prime number.

Can you find some more numbers of this type?

Solution:

We can have:

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

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

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

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

2 x 9 + 1 = 19, which iš a prime number.

2 x 10 + 1 = 23, which is a prime number.

Try These (Page 58)

Question 1.

Find the common factors of

(a) 8, 20

(b) 9, 15

Solution:

(a) 8, 20

Since,

8 = 1 x 8

8 = 2 x 4

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

Again,

20 = 1 x 20

20 = 2 x 10

20 = 4 x 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

Wehave :

9 = 1 x 9

9 = 3 x 3

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

Again, 15 = 1 x 15

15 = 3 x 5

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

From

(i) and

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

Try These (Page 61)

Question 1.

Write the prime factorisations of 16, 28, 38.

Solution:

(i) 16

We have:

Prime factorisationof 16 = 2 x 2 x 2 x 2

(ii) 28

We have:

Prime factorisation of 28 = 2 x 2 x 7

(iii) 38

We have:

Prime factorisation of 38 = 2 x 19

Try These (Page 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

Solution:

(i) 24 and 36

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

Factors of 36 are: 1, 2,3,4,6,9, 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 factor 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 factor 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 factor = 4,

HCF of 12, 16 and 28 = 4