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Instead of actually carrying out a division, it is possible to "test" a number to see if it can be divided exactly by certain numbers.
If a number divides exactly into a number, it is divisible by this number.
24 is divisible by 2, because 24 ÷ 2 is a whole number.
24 is not divisible by 5, because 24 ÷ 5 is not a whole number.
Here is the rule to test divisibility by 11.
Rule for 11
To test a number for divisibility by 11 we must find the sums of alternative digits. This is best illustrated using examples.
Example 1
Determine whether 17281 is divisible by 11.
Method
Underline alternate numbers to get 17226
Add up the underlined digits to get the sum of 1 + 2 + 6 = 9
Add up the non-underlined digits to get the sum of 7 + 2 = 9
If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.
Here they are equal so 17226 is divisible by 11.
Example 2
Determine whether 17281357 is divisible by 11.
Method
Underline alternate numbers to get 17281539
Add up the underlined digits to get the sum of 1 + 2 + 1 + 3 = 7
Add up the non-underlined digits to get the sum of 7 + 8 + 5 + 9 = 29
If these two digit sums are equal or differ by a multiple of 11, the original number is divisible by 11.
Here they differ by 29 - 7 = 22 so 17281539 is divisible by 11.
