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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.

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Q: How do you find out if a number is a multiple of 11?
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