Problems on Divisibility Rules

Problems on divisibility rules will help us to learn how to use the rules to test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

1. Is 7248 is divisible (i) by 4, (ii) by 2 and (iii) by 8?

(i) The number 7248 has 48 on its extreme right side which is exactly divisible by 4. When we divide 48 by 4 we get 12.

Therefore, 7248 is divisible by 4.

(ii) The number 7248 has 8 on its unit place which is an even number so, 7248 is divisible by 2.

(iii) 7248 is divisible by 8 as 7248 has 248 at its hundred place, tens place and unit place which is exactly divisible by 8.

2. A number is divisible by 4 and 12. Is it necessary that it will be divisible by 48? Give another example in support of you answer.

48 = 4 × 12 but 4 and 12 are not co-prime.

Therefore, it is not necessary that the number will be divisible by 48.

Let us consider the number 72 for an example

72 ÷ 4 = 18, so 72 is divisible by 4.

72 ÷ 12 = 6, so 72 is divisible by 12.

But 72 is not divisible by 48.

3. Without actual division, find if 235932 is divisible (i) by 4 and (ii) 8.

(i) The number formed by the last two digits on the extreme right side of 235932 is 32

32 ÷ 4 = 8, i.e. 32 is divisible by 4.

Therefore, 235932 is divisible by 4.

(ii) The number formed by the last three digits on the extreme right side of 235932 is 932

But 932 is not divisible by 8.

Therefore, 235932 is not divisible by 8.