A number when divided by 780 gives remainder 38 .What reminder would be obtained by dividing same number by 26?
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Given:

A number when divided by 780 gives remainder 38.

To find:

The reminder that would be obtained by dividing same number by 26.

Solution:

According to Euclis' division algorithm,

               ...(i)

Where, q is quotient and is the remainder.

It is given that a number when divided by 780 gives remainder 38.

Substituting in (i), we get

So, given number is in the form of , where q is an integer.

On dividing by 26, we get

Since q is an integer, therefore (30q+1) is also an integer but is not an integer. Here 26 is divisor and 12 is remainder.

Therefore, the required remainder is 12.

the answer to the expression is 83