In this article, we will learn about divisibility rule of 11 with examples i.e. how to check if a number is divisible by 11 or not.

What is Divisibility Rule of 11 ?

A number is divisible by 11 if the difference of sum of its digits in odd places and the sum of its digits in even places is equal to zero or completely divisible by 11.

Example 1

Check if 5629 is divisible by 11 or not.
Solution:

We need to check the difference of sum of its digits in odd places and the sum of its digits in even places is equal to zero or completely divisible by 11.
Here, given  number is 5629
Sum of digits at odd places = 5 + 2 = 7 and  sum of digits at even places = 6 + 9 = 15 .
Their difference is 15 – 7 = 8. Since difference is 8 and 8 is not divisible by 11, therefore 5629 is not divisible by 11.

Example 2

Check if 85107 is divisible by 11 or not.
Solution:

We need to check the the difference of sum of its digits in odd places and the sum of its digits in even places is equal to 0 or completely divisible by 11.

Here, given number is 85107.

Sum of digits at odd places = 8 + 1+ 7 = 16

And, sum of digits at even places = 5 + 0 = 5

Difference = 16 – 5 = 11

Since difference is 11 which is divisible by 11, therefore 85107 is divisible by 11.

Example  3

Check if 16803 divisible by 11 or not.
Solution:

We need to check the the difference of sum of its digits in odd places and the sum of its digits in even places is equal to zero or completely divisible by 11.
Here, given  number is 16803.
Sum of digits at odd places = 1 + 8+3 = 12 and  sum of digits at even places = 6+ 0= 6
Their difference = 12 – 6 = 6. Since difference is 6 and 6 is not divisible by 11, therefore 16803 is not divisible by 11

Example 4

Check if 487652 divisible by 11 or not.
Solution:

We need to check the the difference of sum of its digits in odd places and the sum of its digits in even places is equal to zero or completely divisible by 11.
Here, given number is 487652.

Sum of the digits at odd places  = 4 + 7 + 5 = 16
Sum of the digits at even places = 8 + 6 + 2 = 16
Difference between the sum of the digits at odd and even places = 16 – 16, which is 0.
Therefore, 764852 is divisible by 11.