Divisibility Rule of 8 With Examples and FAQ – Mindspark

The divisibility rule of 8 is a shortcut method to check if a number is divisible by 8 or not without performing the lengthy mathematical division process.

What is the Divisibility Rule of 8?

The divisibility rule of 8 tells us if a number can be wholly divided by 8 without leaving any remainder. 

Commonly, we check this with the arithmetic division process. But the divisibility rule of 8 has a shortcut trick to tell us if a number is divisible by 8 or not. 

According to this rule, if the last three digits of a given number are zeroes (000) or if the number formed by the last three digits is completely divisible by 8, then the given number will also be divisible by 8. 

Let us apply this rule to some numbers.

For Example,  let us check the divisibility by 8 on the number 9720.

The number formed by the last three digits is 720.

Upon dividing it by 8, we find that 720 ÷ 8 = 90 (leaves no remainder).

Since the number formed by the last three digits of 9720 is completely divisible by 8. Hence, the given number 9720 is completely divisible by 8.

Similarly, in 31000, the last three digits are zeroes (000), which means that 31000 is also divisible by 8.

Examples

1. Check if the number 7123198 is divisible by 8 or not.

Ans:

The number formed by the last three digits of 7123198 is 198.

Dividing 198 by 8 leaves 6 as a remainder.

Therefore, the given number 7123198 is not divisible by 8.

2. From the numbers given below, select the numbers divisible by 8, using the divisibility rule of 8:

9081000, 5109864, 720

Ans :

First, let’s check the divisibility for 9081000.

We can see that the last three digits of this number are 000. So, as per the rule, 9081000 is divisible by 8.

Now let’s apply the rule on the number 5109864.

The number formed by the last three digits of the number is 864, which will leave no remainder upon dividing by 8. Hence, 5109864 is divisible by 8.

The third number is 720. 

Since it’s a small 3-digit number, we can check for the divisibility by 8 only by dividing this number by 8. 

720 ÷ 8 = 90 (leaves no remainder)

Hence, 720 is divisible by 8.