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:

  1. Add and subtract the digits of N in alternating order.
    It doesn’t matter whether you add or subtract first.
  2. 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.

  1. We add and subtract the digits of 851,327 in alternating order and get -4, as 8-5+1-3+2-7=-4.
  2. 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.

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