**Playing with Numbers **

**Question 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

**Solution:****(a) We have,**

24 = 1 x 24

24 = 2 x 12

24 = 3 x 8

24 = 4 x 6

24 = 6 x 4

Stop here, because 4 and 6 have occurred earlier.

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

**(b) We have,**

15 = 1 x 15

15 = 3 x 5

15 = 5 x 3

Stop here, because 3 and 5 have occurred earlier.

Thus, all the factors of 15 are 1, 3, 5 and 15.

**(c) We have,**

21 = 1 x 21

21 = 3 x 7

21 = 7 x 3

Stop here, because 3 and 7 have occurred earlier.

Thus, all the factors of 21 are 1, 3, 7 and 21.

**(d) We have,**

27 = 1 x 27

27 = 3 x 9

27 = 9 x 3

Stop here, because 3 and 9 have occurred earlier.

Thus, all the factors of 27 are 1, 3, 9 and 27.

**(e) We have,**

12 = 1 x 12

12 = 2 x 6

12 = 3 x 4

12 = 4 x 3

Stop here, because 3 and 4 have occurred earlier.

Thus, all the factors of 12 are 1, 2, 3, 4, 6 and 12.

**(f) We have,**

20 = 1 x 20

20 = 2 x10

20 = 4 x 5

20 = 5 x 4

Stop here, because 4 and 5 have occurred earlier.

Thus, all the factors of 20 are 1, 2, 4, 5, 10 and 20.

**(g) We have,**

18 = 1 x 18

18 = 2 x 9

18 = 3 x 6

18 = 6 x 3

Stop here, because 3 and 6 have occurred earlier.

Thus, all the factors of 18 are 1, 2, 3, 6, 9 and 18.

**(h) We have,**

23 = 1 x 23

23 = 23 x 1

Stop here, because 1 and 23 have occurred earlier.

Thus, all the factors of 23 are 1 and 23.

**(i) We have,**

36 = 1 x 36

36 = 2 x 18

36 = 3 x 12

36 = 4 x 9

36 = 1 x 6

Stop here, because both the factors (6) are same.

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

**Question 2.****Write first five multiples of:(a)** 5

**(b)**8

**(c)**9

**Solution:****(a)** In order to obtain first five multiples of 5, we multiply it by 1, 2, 3, 4 and 5 respectively. ,r

We have,

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4=20

5 x 5 = 25

Hence, the first five multiples of 5 are 5, 10, 15, 20 and 25 respectively.

**(b)** In order to obtain first five multiples of 8, we multiply it by 1, 2, 3, 4 and 5 respectively.

We have,

8 x 1=8

8 x 2=16

8 x 3=24

8 x 4 = 32

8 x 5 = 40

Hence, the first five multiples of 8 are 8, 16, 24, 32 and 40 respectively,

**(c)** In order to obtain first five multiples of 9, we multiply it by 1, 2, 3, 4 and 5 respectively.

We have,

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

Hence, the first five multiples of 9 are 9, 18, 27, 36 and 45 respectively.

**Question 3.****Match the items in column 1 with the items in column 2.**

**Solution:**

Matching is as under :

**(i)**→ (c) ∵ 35 x 2 = 70

**(ii)**→(d) ∵ 30 = 15 = 2

**(iii)**→ (a) ∵ 8 x 2 = 16

**(iv)**→ (f) ∵ 20 = 20 = 1

**(v)**→ (e) ∵ 50 = 25 = 2

**Question 4.****Find all the multiples of 9 upto 100.**

**Solution:**

All the multiples of 9 upto 100 are

9 x 1, 9 x 2, 9 x 3, 9 x 4, 9 x 5, 9 x 6, 9 x 7, 9 x 8, 9 x 9, 9 x 10 and 9 x 11.

i. e., 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 and 99.