In the given number, if the sum of the digits in odd places and sum of the digits in even places differ by zero or a number divisible by 11, then the given number is divisible by 11.
Example 1 :
Check whether 762498 is divisible by 11.
Solution :
In the given number 762498,
Sum of the digits in odd places = 7 + 2 + 9
Sum of the digits in odd places = 18
In the given number 762498,
Sum of the digits in even places = 6 + 4 + 8
Sum of the digits in even places = 18
The difference between the sum of the digits in odd places and sum of the digits in even places is
= 18 - 18
= 0
Sum of the digits in odd places and sum of the digits in even places differ by zero.
So the given number 762498 is divisible by 11.
Example 2 :
Check whether 473 is divisible by 11.
Solution :
In the given number 473,
Sum of the digits in odd places = 4 + 3
Sum of the digits in odd places = 7
In the given number 473, there is only one digit ion even place. That is 7.
Then, we have
Sum of the digits in even places = 7
The difference between the sum of the digits in odd places and sum of the digits in even places is
= 7 - 7
= 0
Sum of the digits in odd places and sum of the digits in even places differ by zero.
So the given number 473 is divisible by 11.
Example 3 :
Check whether 85965 is divisible by 11.
Solution :
In the given number 85965,
Sum of the digits in odd places = 8 + 9 + 5
Sum of the digits in odd places = 22
In the given number 85965,
Sum of the digits in even places = 5 + 6
Sum of the digits in even places = 11
The difference between the sum of the digits in odd places and sum of the digits in even places is
= 22 - 11
= 11
Sum of the digits in odd places and sum of the digits in even places differ by 11 which is divisible by 11.
So, the given number 85965 is divisible by 11.
Example 4 :
Check whether 190817 is divisible by 11.
Solution :
In the given number 190817,
Sum of the digits in odd places = 1 + 0 + 1
Sum of the digits in odd places = 2
In the given number 190817,
Sum of the digits in even places = 9 + 8 + 7
Sum of the digits in even places = 24
The difference between the sum of the digits in odd places and sum of the digits in even places is
= 24 - 2
= 22
Sum of the digits in odd places and sum of the digits in even places differ by 22 which is divisible by 11.
So, the given number 190817 is divisible by 11.
Example 5 :
Check whether 6368 is divisible by 11.
Solution :
In the given number 6368,
Sum of the digits in odd places = 6 + 6
Sum of the digits in odd places = 12
In the given number 6368,
Sum of the digits in even places = 3 + 8
Sum of the digits in even places = 11
The difference between the sum of the digits in odd places and sum of the digits in even places is
= 12 - 11
= 1
Sum of the digits in odd places and sum of the digits in even places differ by 1 which is not divisible by 11.
So, the given number 6368 is divisible by 11.
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