**Playing with Numbers**

**Exercise 3.4**

1). Find the common factors of :

(a) 20 and 28

Factors of 20 = 1, 2, 4, 5, 10, 20

Factors of 28 = 1, 2, 4, 7, 14, 28

Common factors = 1, 2, 4

(b) 15 and 25

Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

Common factors = 1, 5

(c) 35 and 50

Factors of 35 = 1, 5, 7, 35

Factors of 50 = 1, 2, 5, 10, 25, 50

Common factors = 1, 5

(d) 56 and 120

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 22, 30, 40, 60,

120

Common factors = 1, 2, 4, 8

2). Find the common factors of :

(a) 4, 8 and 12

Factors of 4 = 1, 2, 4

Factors of 8 = 1, 2, 4, 8

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

Common factors = 1, 2, 4

(b) 5, 15 and 25

Factors of 5 = 1, 5

Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

Common factors = 1, 5

3). Find first three common multiples of :

(a) 6 and 8

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84,

90, 96, 102, . . . . . .

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104,

112, 120, . . . . . . .

First three common multiples are = 24, 48, 72

(b) 12 and 18

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .

Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . .

First, three common multiples are = 36, 72, 108

4). Write all the numbers less than 100 which are common multiples of 3 and 4.

To find the common multiples of 3 and 4 we multiply 3 and 4

3 X 4 = 12

Multiples of 12 are = 12, 24, 36, 48, 60, 72, 84, 96

Therefore, common multiples of 3 and 4 less than 100 = 12, 24,

36, 48, 60, 72, 84, 96

5). Which of the following numbers are co-prime?

(a) 18 and 35

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 35 = 1, 5, 7, 35

Common factors= 1

Therefore, 18 and 35 are co-prime numbers.

(b) 15 and 37

Factors of 15 = 1, 3, 5, 15

Factors of 37 = 1, 37

Common factors= 1

Therefore, 15 and 37 are co-prime numbers.

(c) 30 and 415

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

Factors of 415 = 1, 5, 83, 415

Common factors= 1 , 5

Therefore, 30 and 415 are not co-prime numbers.

(d) 17 and 68

Factors of 17 = 1, 17

Factors of 68 = 1, 2 , 4, 17, 34, 68

Common factors= 1, 17

Therefore, 17 and 68 are not co-prime numbers.

(e) 216 and 215

Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108,

216

Factors of 215 = 1, 5, 43, 215

Common factors= 1

Therefore, 216 and 215 are co-prime numbers.

(f) 81 and 16

Factors of 81 = 1, 3, 9, 27, 81

Factors of 16 = 1, 2, 4, 8, 16

Common factors= 1

Therefore, 81 and 16 are co-prime numbers.

6). A number is divisible by both 5 and 12. By which other numbers will that number be always divisible?

If a number is divisible by both 5 and 12 then the number is multiple of 5 X 12 = 60.

The other number that divides the multiples of 60 are 2, 3, 4, 6.

(factors of 5 and 12)

7). A number is divisible by 12. By what other numbers will that number be divisible?

If a number is divisible by 12, then it is also divisible by the factors of 12 that are 2, 3, 4, 6.