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.