# A number when div

Given: A number when divided by 143 leaves 31 as remainder.

To find:  the remainder when the same number is divided by 13.

Solution:

Let the number be a.

By Euclid’s division lemma -

Putting the values of divisor as 143 and remainder as 31.

a = 143(q) + 31, where q is the quotient when divided by 143.

a = {13(11)}q + 31

a = 13(11)q + 13(2) + 5

a = 13(11q + 2) + 5 ..... (i)

Again when it is divided by 13, let the remainder be r.

So, a = 13(p) + r ......(ii)

where p is the quotient when divided by 13.

Comparing (i) and (ii) -

11q + 2 = p and r = 5.

So remainder = 5.

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