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In this topic divisibility by 11 first let us see the definition.
If the difference between the sum of one set of alternate digits and the sum of the other set of alternate digits is 0 or 11 or 22.....the numbers are divisible by 11.

Consider the numbers 121,132,143,154,165,176,187,198 all these numbers are divisible by 11.

In 121 , 1 + 1 = 2[Which is equal to the middle number]

In 143 , 1 + 3 = 4[Which is equal to the middle number]

In 165 , 1 + 5 = 6[Which is equal to the middle number]

Example 1:

Test whether 198 is divisible by 11?

In this three digit number the sum of the first and last number = middle number that is 1 + 8 = 9
So the whole number 198 is divisible by 11.

Example 2:

Test whether 473 is divisible by 11?

In this three digit number the sum of the first and last number = middle number that is 4 + 3 = 7
So the whole number 473 is divisible by 11.
Consider the following 4 digit numbers which are divisible by 11 2563,3498,5137,6369.

In 2563 , 2 + 6 = 8 , 5 + 3 = 8 , 8 - 8 = 0

In 3498 , 3 + 9 = 12 , 4 + 8 = 12 , 12 - 12 = 0

In 5137 , 5 + 3 = 8 , 1 + 7 = 8 , 8 - 8 = 0

Let us see another example to test divisibility by 11

Example 3:

Test whether 6369 is divisible by 11?

In this four digit number the sum of the first and last number = middle number that is 6 + 6 = 12, 3 + 9 =12 , 12 - 12 = 0
So the whole number 6369 is divisible by 11.
In the following worksheet in this page, 'Divisibility by 11,' you can find 5 questions in the form of a quiz and you can get direct answers too.