# Secret Number Trick # 2

If you thought testing divisibility of a number by 7 was a blast, you won’t believe how easy it is to test **divisibility by 11**.

Suppose you are given a number *N*. To check divisibility of *N* by 11:

**Add**and**subtract**the digits of*N*in**alternating order**.

It doesn’t matter whether you add or subtract first.- Check whether the resulting number is divisible by 11. If so, then
*N*is divisible by 11 as well, otherwise it isn’t.

The way I memorize this trick is by just repeating “*add and subtract, add and subtract, add and subtract*“.

Let us look at an **example**.

Say we are given 851,327 and want to see whether 11 divides this.

- We
**add**and**subtract**the digits of 851,327 in**alternating order**and get -4, as 8-5+1-3+2-7=-4. - But -4 isn’t divisible by 11, and so 851,327 isn’t either.

If you are interested in why this method works, check out this proof.