Question

Using Euclid's division algorithm, find which of the following pairs of numbers are co-primes: 616,309

Answer 1

ANSWER

Given, the two numbers 847,2160

Here, Co-primes are 2 numbers which have only one as a common factor.

Let, a=2160

b=847

Then, by Euclid's lemma

a=bq+r,0≤r<b

So,

2160=847×2+466

847=466×1+381

466=381×1+85

381=85×4+41

85=41×2+3

41=3×13+2

3=2×1+1

2=1×2+0

As 1 is the H.C.F of 847 and 2160,

∴ 847 and 2160 are co-primes as they have only 1 as their H.C.F.