The divisibility rule for 11 is very similar to the divisibility rules for 7 and 13, except that it's much easier to work with.

Here it is: Alternate adding and subtracting the digits, and if the result is a multiple of 11, then the original number is a multiple of 11.

Here are some examples:

165: 1 - 6 + 5 = 0, and 0 is a multiple of 11.

61,391: 6 - 1 + 3 - 9 + 1 = 0, so the 61,391 is a multiple of 11

191,906: 1 - 9 + 1 - 9 + 0 - 6 = -22, which is a multiple of 11.

One interesting thing about this is that several powers of 11 are palindromes: 121, 1331, 14641, and it's interesting to see how those digits all cancel each other out when you alternately add and subtract.