Library/Number Theory/Divisibility rules/Divisibility rules for 11

Divisibility rules for 11

Overview

Divisibility by 11

A number is divisible by 1111 iff the alternating sum of its digits is divisible by 1111.

If the number has digits d1d2…dnd_1d_2\ldots d_n (from left to right), compute:

(d1−d2+d3−d4+⋯ )(d_1 - d_2 + d_3 - d_4 + \cdots)

The original number is divisible by 1111 iff this alternating sum is divisible by 1111.

Example

  • 9 5159\,515: 9−5+1−5=09-5+1-5 = 0, so 9 5159\,515 is divisible by 1111.