PROBLEMS ON FACTORS AND MULTIPLES

Problem 1 :

Is 8 a factor of 24 ?

Solution :

24 ÷ 8 = 3 (Remainder is 0)

24 = 8 x 3

When dividing 24 by 8, we get the remainder as 0. Then 3 is a factor of 24.

Problem 2 :

Is 5 a factor of 43 ?

Solution :

When we divide 43 by 5, we get quotient as 8 and remainder as 3. So, it is not divisible by 5.

Hence 5 is not a factor of 43.

Problem 3 :

Is 7 a factor of 34 ? 

Solution :

When we divide 34 by 7, we get quotient = 4 and remainder as 6. Since the remainder is not 0, it is not divisible by 7.

So, 7 is not a factor of 34.

Problem 4 : 

Is 9 a factor of 72 ?

Solution :

When we divide 72 by 9, we get 8 as quotient and 0 as remainder. Then 9 is a factor of 72.

72 = 8 x 9

9 is the factor of 72.

Problem 5 :

List all factors of 20.

Solution :

20 = 1 x 20

20 = 2 x 10

20 = 4 x 5

So, factors of 20 are 1, 2, 4, 5, 10 and 20.

Problem 6 :

Write the largest factor of (other than itself) 

a)  14   b)  27    c)  56   d)  44     e)  75   f)  90

Solution :

For every natural numbers there must be two factors 1 and itself. So, the smallest factor of the number is 1 and largest factor the number is itself.

a)  14

Factor of 14 = 1, 2, 7, 14

Largest factor of 14 other than itself is 7.

b)  27

Factor of 27 = 1, 3, 9, 27

Largest factor of 27 other than itself is 9.

c)  56

Factor of 56 = 1, 2, 4, 7, 8, 14, 28 and 56

Largest factor of 56 other than itself is 28.

d)  44

Factor of 44 = 1, 2, 11, 22 and 44.

Largest factor of 44 other than itself is 22.

e)  75

Factor of 75 = 1, 3, 5, 15, 25 and 75

Largest factor of 75 other than itself is 25.

f)  90

Factor of 90 = 1, 3, 5, 10, 15, 30 and 90

Largest factor of 90 other than itself is 30.

Problem 7 :

Buses arrive at a sports stadium every 8 minutes and train arrives every 14 minutes. A bus and a train have just arrived simultaneously. How long will it be before this happens again ?

Solution :

Buses will arrive every 8 minutes, the time interval

= 8, 16, 24, 32, 40, 48, 56...............

Trains will arrive every 14 minutes, the time interval

= 14, 28, 42, 56, ...................

After 56 minutes only the bus and train will arrive the stadium 

= 56 - 8

= 48 minutes

So, after 48 minutes both bus and train will arrive the stadium.

Problem 8 :

List the first six multiples of 

a)  4      b)  9     c)  10     d)  15    e) 22    f)  35

Solution :

a) Multiples of 4 :

4, 8, 12, 16, 20, 24, ..............

b) Multiples of 9 :

9, 18, 27, 36, 45, 54, ..............

c) Multiples of 10 :

10, 20, 30, 40, 50, 60, ..............

d) Multiples of 15 :

15, 30, 45, 60, 75, 90, ...............

e) Multiples of 22 :

22, 44, 66, 88, 110, 132, ...........

f) Multiples of 35 :

35, 70, 105, 140, 175, 210, ............

Problem 9 :

Find the 

a) seventh multiple of 6

b) sixth multiple of 11

c)  eleventh multiple of 15

d) hundredth multiple of 99.

Solution :

a) seventh multiple of 6

7^th multiple = 7 x 6 ==> 42

So, 42 is the 7^th multiple of 6.

b) sixth multiple of 11

6^th multiple = 11 x 6 ==> 66

So, 66 is the 6^th multiple of 6.

c)  eleventh multiple of 15

11^th multiple of 15 = 11 x 15 ==> 165

So, 165 is the 11^th multiple of 15.

d) hundredth multiple of 99.

100^th multiple of 99= 100 x 99 ==> 9900

So, 9900 is the 100^th multiple of 99.

Problem 10 :

a) Find the smallest multiple of 7 that is greater than 500

b)  Find the greatest multiple of 12 that is less than 1000.

Solution :

a) 

70 x 7 ==> 490

72 x 7 ==> 504

So, the smallest multiple of 7 and that is greater than 500 is 504.

b) 

12 x 80 = 960

12 x 83 = 996

So, the largest multiple of 12 and it is less than 1000 is 996.