Without performing actual division, find the remainder when 928174653 is divided by 11.

Given:

928174653 is divided by 11.

To do:

We have to find the remainder when 928174653 is divided by 11.

Solution:

We know that,

A number is divisible by 11 if the difference of the sum of its alternate digits is 0 or divisible by 11.

Here,

In the number 928174653,

The difference of the sum of its alternate digits is $(9+8+7+6+3)-(2+1+4+5)=33-12=21$.

Therefore,

When 928174653 is divided by 11, then the remainder is $21-11=10$.