Sign of divisibility by 11

There are other signs of divisibility other than those listed, but they are an order of magnitude more complicated. For those who are interested, we give an example of the sign of divisibility at 11.

Sign of divisibility by 11

The number is divided by 11, if the sum of the digits that stand in even places is equal to the sum of digits standing in odd places, or differs from it by 11.

In fact, the sign of divisibility by 11 is very interesting, let's try to figure it out with an example:

• Check if 671 is divisible by 11.

So, the numbers that stand in odd places are 6 (standing in first place) and 1 (standing in third place). The number that stands in an even place is 7 (it stands in second place). 6 + 1 = 7. The sum of the figures standing on an odd place is equal to the sum of the numbers on an even place, which means that 671 is divided by 11.

• Check if 3905 is divided by 11.

The numbers that stand in odd places are 3 (in the first place) and 0 (in the third place). The numbers that stand in an even place are 9 (stands in second place) and 5 (stands in fourth place).

3 + 0 ≠ 9 + 5 → 3 ≠ 14 The sum of digits standing in an odd place is not equal to the sum of digits in an even place, but the sum of digits differ exactly by 11. 14 - 3 = 11. So 3905 is divided by 11.