Divisible by 11?

Add alternate digits, subtract the two groups, look for 0 or 11.

The question

Is 8,514 divisible by 11?

The trick

Add the digits in odd positions, add the digits in even positions, then subtract. If you get 0 or a multiple of 11, the number divides by 11.

Worked example

1Odd positions (1st and 3rd): 8 + 1 = 9
2Even positions (2nd and 4th): 5 + 4 = 9
3Subtract: 9 − 9 = 0
40 is a multiple of 11, so 8,514 is divisible by 11

So: Yes

Remember it like this

Zig-zag along the digits: plus, minus, plus, minus. If the zig-zag total lands on zero or eleven, eleven fits.

In the exam

A negative result is fine — you only care about the size. 2,915 gives 3 − 14 = −11, which is a multiple of 11, so it divides. Don't discard it just because of the minus sign.

Why it works

Powers of 10 alternate between leaving remainder 1 and remainder −1 when divided by 11. That alternation is exactly what the plus-minus grouping captures.

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