To find out if an integer is

divisible by

11:

Consider the integer a where

a = a_{n}10^{n} + a_{n-1}10^{n-1} +...+ a_{1}10^{1} + a_{0}

11 divides a if and only if the alternating sum of the digits (-1)^{n}a_{n} + (-1)^{n-1}a_{n-1} + ... - a_{1} + a_{0} is divisible by 11.

eg. Is 152328 divisible by 11?

Observe -1 + 5 - 2 + 3 - 2 + 8 = 11

11 obviously divides 11, therefore 152328 is divisible by 11.