If the alternating sum of the digits is divisible by eleven, so is the number.

For example, 1639 leads to 9 - 3 + 6 - 1 = 11, so 1639 is divisible by 11.

Proof:

Every integer n can be expressed as n = a1*(10^k) + a2*(10^k-1)+ .....+ a_k+1 where a1, a2, a3, ...a_k+1 are integers between 0 and 9. 10 is congruent to -1 mod(11). Thus if (-1^k)*a1 + (-1^k-1)*a2 + ...+ (a_k+1) is congruent to 0mod(11) then n is divisible by 11.