Question

a number which when divided by 143 leaves 31 as a remainder . what will be the remainder when the same number is divided by 13?

Answer 1

when we divided the same number by 13 we got a remainder 11

Answer 2

Answer:

We know that,

Dividend = Divisor × Quotient + Remainder (by Euclid's division lemma)

It is given that:

Divisor = 143

Remainder = 13

So, the given number is in the form of 143x + 31, where x is the quotient.

∴ 143x + 31 = 13 (11x) + (13 × 2) + 5

                    = 13 (11x + 2) + 5  

Thus, the remainder will be 5 when the same number is divided by 13.