Did you know that a positive integer is evenly divisible by 11 if and only if the alternating sum of it's digits is evenly divisible by 11? Well, it's a fact, just look around: 121 -> 0, 108152 -> 11, 9090909091 -> 44, 1909090909 -> -44, etc. but 98 -> 1, 7889 -> -2, 123456789 -> -5, etc.
11 909090909080909090909 1331 123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
11 is divisible by 11. 909090909080909090909 is not divisible by 11. 1331 is divisible by 11. 123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 is not divisible by 11.