The fast method
⚡
(1 + 1) - 2 = 0.
How it works
Subtract the sums of alternate digits. A multiple of 11, including zero, means the integer is divisible by 11. 10 is congruent to -1 modulo 11, so powers of 10 alternate between 1 and -1.
Why it works
10 is congruent to -1 modulo 11, so powers of 10 alternate between 1 and -1.
Use it when
Applies to base-ten integers. Either alternating group can be subtracted from the other.
Watch out for
Zero and negative multiples of 11 also pass the test.
Verified examples
Example 1
Is 121 divisible by 11?
(1 + 1) - 2 = 0.
YesExample 2
Is 2728 divisible by 11?
(2 + 2) - (7 + 8) = -11.
YesExample 3
Is 1234 divisible by 11?
(1 + 3) - (2 + 4) = -2.
No