Divisible By 11: Rules, Examples and FAQ – Mindspark

A number is divisible by 11 if it leaves zero as the remainder when divided by 11. Here we will understand the divisibility rule of 11 with some examples.

How to find if a number is divisible by 11?

The divisibility rule of 11 tells us if a number can be wholly divided by 11 without leaving any remainder.

Usually, we check this by dividing the given number by 11. But the divisibility rule of 11 has a shortcut method to tell if a number is divisible by 11 or not.

To apply this rule, we add the digits at odd and even places of the given number. Then we calculate the difference between both the results. If the difference is zero or a multiple of 11, we confirm that the given number is also divisible by the number 11. For finding the difference, we always subtract the smaller sum from the larger sum.

Let us clear this with an example.

Example – Let us apply the divisibility rule of 11 on the number 1331.
In the given number, digits at odd places = 1, 3 and digits at even places = 3, 1.
Sum of digits at odd places = 1 + 3 = 4 and sum of digits at even places = 3 + 1 = 4
Difference = 4-4 = 0
Since the difference obtained is zero, we can confirm that 1331 is divisible by the number 11.

Now, let us do this operation on a large number, 162272.
In the given number,
Sum of digits at odd places = 1 + 2 + 7 = 10
Sum of digits at even places = 6 + 2 + 2 = 10
Difference = 10 – 10 = 0
Since the difference is 0, so the number 162272 is divisible by the number 11.

Examples

1. Using the divisibility rule of 11, check whether the number 25110 is divisible by 11?

Ans:

Let us check if 25110 is divisible by the number 11 or not?

Sum of digits at odd places = 2 + 1 + 0 = 3

Sum of digits at even places = 5 + 1 = 6

Difference = 6 – 3 = 3

Since the difference is 3, which is not a multiple of 11, the number 25110 is not divisible by the number 11.

2. Which number is divisible by 11? (a) 1510 (b) 1452 (c) 1010 (d) 1121

Calculate the sum of the digits at odd places and even places of the number.  If the sum difference is 0 or divisible by the number 11, the given number is divisible by 11. So, let’s check each number one by one.

a. 1510

Difference between sum of digits at odd places and even places

= (5 + 0) – (1 + 1) = 5 – 2 = 3

Therefore, 1516 is not divisible by the number 11. 

b. 1452

Difference between sum of digits at odd places and even places

= (1 + 5) – (4 + 2) = 6 – 6 = 0

Therefore, 1452 is divisible by the number 11.

c. 1011

Difference between sum of digits at odd places and even places

= (1 + 1) – (0 + 1) = 2 – 1 = 1

Therefore, 1010 is not divisible by the number 11.

d. 1121

Difference between sum of digits at odd places and even places

= (1 + 2) – (1 + 1) = 3 – 2 = 1

Therefore, 1121 is not divisible by the number 11.