## DIVISIBILITY BY 11

Divisibility by 11 :

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.

By considering 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?

Solution :

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 ?

Solution :

In the given number 473, the sum of the first and last number = middle number that is 4 + 3 = 7.

Hence, the whole number 473 is divisible by 11.

By considering the following 4 digit numbers 2563, 3498, 5137, 6369.

The above four digit numbers are divisible by 11.

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

Example 3 :

Test whether 6369 is divisible by 11 ?

Solution :

In the given four digit number 6369, the sum of the first and last number = middle number that is 6 + 6 = 12, 3 + 9 =12 , 12 - 12 = 0

Hence, the given number 6369 is divisible by 11.

After having gone through the stuff given above, we hope that the students would have understood "Divisibility by 11"

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