What is the divisibility rule for 11?

Answer 1

Add together all the digits in odd positions in the integer (the 1st, 3rd, 5th, etc). Answer = X.Add together all the digits in even positions in the integer. Answer = Y.

If X - Y is a multiple of 11 (including negative multiples and 0) then the integer is divisible by 11.

Answer 2

If you sum every second digit and then subtract all other digits and the answer is zero or a multiple of 11. Starting from the first digit, add all the alternate digits to obtain sum S1. Now add up the remaining digits (that were not added in S1) to get S2. Find the difference S1 - S2 (or S2 - S1). If the result is divisible by 11 the number itself will also be divisible by 11.

Note that 0 is considered divisible by 11 (or any other numbers except zero)

Eg.: To see whether 365167484is divisible by 11

We get S1 = 3+5+6+4+4 = 22

Also S2 = 6+1+7+8 = 22

So S1-S2 = 0 hence 365167484 is divisible by 11 (365167484 / 11 = 33197044)

1. Add the odd-numbered digits together (the first, third, fifth, etc).

2. Add the even-numbered digits together (the second, fourth, sixth, etc).

3. Subtract the smaller number from the bigger number. If the number you get is divisible by 11, then so is the original number. (0 is divisible by 11).

Example: Is 60258 divisible by 11?

1. 6 + 2+ 8 = 16

2. 0 + 5 = 5

3. 16-5 = 11. So yes, 60258 is divisible by 11

11

If you sum every second digit and then subtract all other digits and the answer is:

• 0, or
• divisible by 11

1364 ((3+4) - (1+6) = 0) Yes

3729 ((7+9) - (3+2) = 11) Yes

25176 ((5+7) - (2+1+6) = 3) No