# DIVISIBILITY BY 11 - RULE WITH EXPLANATION, SOLVED EXAMPLES

Multiplication Tables
and
Division before Divisibility By 11
They are prerequisites here.

Here we study methods that can be used to determine
whether a number is evenly divisible by 11.

These are shortcuts for testing a number's factors
without resorting to division calculations.

The rules given below transform a given number's divisibility
by a divisor to a smaller number's divisibility by the same divisor.

If the result is not obvious after applying it once,
the rule should be applied again to the smaller number.

We present the rules with examples, in a simple way,
to follow, understand and apply.

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## Rule of Divisibility By 11

To find out, if a number is divisible by 11, take the sum of the digits at odd places, and the sum of the digits at even places, and subtract one from the other. If you get an answer divisible by 11 (including zero), then the original number is divisible by 11.
If you don't know the new number's divisibility, you can apply the rule again.(usually, it is not required to apply again.)

Example 1 of Divisibility Rule for 11

Find whether 65714 is divisible by 11 or not.

Solution :
sum of alternate digits = 6 + 7 + 4 = 17; sum of remaining digits = 5 + 1 = 6;
Subtracting, 17 - 6 = 11 is divisible by 11.
∴ 65714 is divisible by 11. Ans.

Example 2 of Rule of Divisibility By 11

Find whether 123453 is divisible by 11 or not.

Solution :
sum of alternate digits = 1 + 3 + 5 = 9; sum of remaining digits = 2 + 4 + 3 = 9;
Subtracting, 9 - 9 = 0.
∴ 123453 is divisible by 11. Ans.

Example 3 of Rule of Divisibility By 11

Find whether 5232819 is divisible by 11 or not.

Solution :
sum of alternate digits = 5 + 3 + 8 + 9 = 25; sum of remaining digits = 2 + 2 + 1 = 5;
Subtracting, 25 - 5 = 20 is not divisible by 11.
∴ 5232819 is not divisible by 11. Ans.

Example 4 of Rule of Divisibility By 11

Find whether 58976544 is divisible by 11 or not.

Solution :
sum of alternate digits = 5 + 9 + 6 + 4 = 24; sum of remaining digits = 8 + 7 + 5 + 4 = 24;
Subtracting, 24 - 24 = 0 is divisible by 11.
∴ 58976544 is divisible by 11. Ans.

Example 5 of Rule of Divisibility By 11

Find whether 914510876 is divisible by 11 or not.

Solution :
sum of alternate digits = 9 + 4 + 1 + 8 + 6 = 28; sum of remaining digits = 1 + 5 + 0 + 7 = 13;
Subtracting, 28 - 13 = 15 is not divisible by 11.
∴ 914510876 is not divisible by 11. Ans.

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