Positive or
negative integers of course; otherwise "divides" isn't as
meaningful.
Take a
number you'd hate to
divide out
longhand: 1,358,024,668.
Add its first
digit to its third to its fifth
etc. till there are no more: 1 + 5 + 0 + 4 + 6 = 16.
Repeat with the even digits: 3 + 8 + 2 + 6 + 8 = 27.
Subtract the larger number from the smaller. If the result is 11 or 0, your number is divisible by eleven, otherwise not. In this case, 27 - 16 = 11, so 1,358,024,668 IS divisible by
eleven.
Mathematics is
deeper and more
beautiful than most of us will ever know.