Divisibility Rules for 11

A number is divisible by 11 if the sum of digits at odd and even places are equal or differ by a number divisible by 11.

Rule 1:

In this Divisibility Rule for 11, Subtract the last digit from the remaining leading truncated number. If the result is divisible by 11, then so was the first number. Apply this rule over and over again as necessary.

Example: 19151 → 1915-1 =1914 → 191-4=187 → 18-7=11,

so yes, 19151 is divisible by 11.

Rule 2:

In this Divisibility Rule for 11, we start from the right and add every second digit. Now subtract from that total the sum of the remaining digits. The resulting number is divisible by 11 if and only if the number you started with is divisible by 11.

For example consider 678234.

(4 + 2 + 7) – (3 + 8 + 6) = 13 – 17 = -4

which is not divisible by 11 so 678234 is not divisible by 11.

Now try 908193

(3 + 1 + 0) – (9 + 8 + 9) = -22

which is divisible by 11 so 908193 is divisible by 11.

Some Basic Concept on Divisibility Rules for 11 which will help you solve quickly:

If the difference of the sum of the digits at odd places and the sum of the digits at even places is 0 or divisible by 11.

Example: 1364 ((3 + 4) – (1 + 6) = 0) Yes
25176 ((5 + 7) – (2 + 1 + 6) = 3) No

Any six-digits, twelve-digits, eighteen-digits or any such number with number of digits equal to multiple of 6, is divisible by each of 7, 11 and 13 if all of its digits are same.
For example 666666, 888888, 333333333333 are all divisible by 7, 11 and 13.

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