Divisibility Rule for 11

If you divide a number by 11 and you get a whole number as an answer (quotient), then that number is divisible by 11.

Instead of simply dividing your number by 11 to see if you get a whole number, you can use what we call the Divisibility Rule for 11.

The Divisibility Rule for 11 is used to determine if a number is divisible by 11. You can also call it the test of divisibility for 11.

To determine if a number is divisible by 11, alternate subtracting and adding the digits in the number. If the result is divisible by 11, then the number is divisible by 11.

For example, to determine if 123,456 is divisible by 11, calculate 1 - 2 + 3 - 4 + 5 - 6 = -3. Since -3 is not divisible by 11, neither is 123,456.

However, 828,487 is divisible by 11 because 8 - 2 + 8 - 4 + 8 - 7 = 11 and 11 is divisible by 11.

Note that when you do these calculations and you get a negative number like -3 above, you can ignore the minus when figuring out if it is divisible by 11. For example if the result was -22, then the number would be divisible by 11 because 22 is divisible by 11.

Divisibility Rule for 12
Here is the next Divisibility Rule on our list.

Divisibility Rules
Here is a list of all our Divisibility Rules.