Understand the Rule for Divisibility by 11

Instead of actually carrying out a division, it is possible to test a number to see if it can be divided exactly by certain numbers.

If a number divides exactly into a number, it is divisible by this number.

24 is divisible by 2, because 24 ÷ 2 is a whole number.

24 is not divisible by 5, because 24 ÷ 5 is not a whole number.

Here is the rule to test divisibility by 11.

Rule for 11

To test a number for divisibility by 11, we must find the sum of alternate digits.  This is best illustrated using examples.

Example 1

Determine whether 17,281 is divisible by 11.

Method

Underline alternate numbers to get 17226

Add up the underlined digits to get the sum of 1 + 2 + 6 = 9

Add up the non-underlined digits to get the sum of 7 + 2 = 9

If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.

Here they are equal, so 17,226 is divisible by 11.

Example 2

Determine whether 17,281,357 is divisible by 11.

Method

Underline alternate numbers to get 17281539

Add up the underlined digits to get the sum of 1 + 2 + 1 + 3 = 7

Add up the non-underlined digits to get the sum of 7 + 8 + 5 + 9 = 29

If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.

Here they differ by 29 - 7 = 22 so 17,281,539 is divisible by 11.

That's a pretty useful tip, isn't it?!

Let's get to work!