Say you want to know whether 586021491 is evenly divisible by 11.
Add up every other digit: 5 + 6 + 2 + 4 + 1 = 18 Add up the other digits: 8 + 0 + 1 + 9 = 18
If those numbers are the same, or the difference between them is a multiple of 11, then the original number is a multiple of 11 too!
Intuitive explanation: see, every time you add 11 or 110 or 1100 etc. to a number without any "carrying" it always contributes 1 to each of those two groups defined above, so the difference between them stays the same. Whereas a "carry" operation removes ten from one group and adds one to the other, which still keeps the difference between the groups a multiple of 11.
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