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.