Question

A number when divided by 259 leaves a remainder 139. What will be the remainder when the same number is divided by 37?

Answer 1

Hint- Here we will proceed by assuming the dividend be n and quotient be q. Then we will use a division algorithm to get the required number.
Euclid’s division algorithm – It is an algorithm which, given two integers N and D, computes their quotient or remainder.
$ \Rightarrow$ Dividend = Divisor $\times$ Quotient + Remainder

Complete step-by-step answer:
Let the dividend be n.
Let the quotient be q.
According to the division algorithm,
Dividend = (Divisor x Quotient) + Remainder
$\Rightarrow$ Dividend = (259q) + 139
$\Rightarrow$ n = (259q) + 139
Dividend is the same in both cases. So,
$\Rightarrow$ n = 37(7q) + 111 + 28
$\Rightarrow$ n = 37(7q) + 3(37) + 28
$\Rightarrow$ n = 37(7q + 3) + 28
Thus the remainder is 28.
Hence the number when the same number divided by 37 is 28.

Note- While solving this question, we must know about the Euclid’s division algorithm i.e. It is an algorithm which, given two integers N and D, computes their quotient or remainder. Also this algorithm is used in similar questions also.