How to tell if a number is divisible by 11

The rule schools teach for 11 alternates plus and minus along the digits and often lands on a negative number, which throws children off. There is a friendlier version that is nothing but one addition.

How to check it

1. Starting from the right-hand end, split the number into blocks of two digits. An odd leading digit is left alone at the front.
2. Add the blocks together.
3. If the total is more than two digits, split and add again.
4. If the final total is 0, 11, 22, 33 … 99, the number divides by 11.

Worked examples

The version taught at school: plus and minus

Write alternating signs along the digits and add them up: for 4620 that is +4 −6 +2 −0 = 0. Landing on 0 or any multiple of 11 means the number divides by 11.

The sign of the answer does not matter: −11 counts exactly as 11 does. That is the part that confuses people, and the reason the pair version is easier to trust.

Both rules are the same fact seen from different distances, so they never disagree. Use whichever you find quicker.

Why pairing works

Every hundred is 99 + 1, and 99 is nine 11s. So each two-digit block above the last contributes its own value plus a pile of 11s that can be ignored.

That makes it exactly the rule for 9 one size up: for 9 you add single digits because every ten is 9 + 1; for 11 you add pairs because every hundred is 99 + 1.

The pairs have to be cut from the right. 45 815 is 4 | 58 | 15, never 45 | 81 | 5. Cutting from the left gives the wrong answer.

Where it goes wrong

• Pairing from the left. The blocks must start at the units end.
• Rejecting a negative total in the plus-and-minus version. −11 means yes.
• Forgetting that 0 counts as a multiple of 11. A total of 0 is a pass.

Questions people ask

Related rules

• How to tell if a number is divisible by 9
• How to tell if a number is divisible by 3