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 __1__7__2__2__6__

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 __1__7__2__8__1__5__3__9

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!