To find out if an integer is
divisible by
11:
Consider the integer a where
a = an10n + an-110n-1 +...+ a1101 + a0
11 divides a if and only if the alternating sum of the digits (-1)nan + (-1)n-1an-1 + ... - a1 + a0 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.