Question

use euclids devision algorithm to find whether the pair of numbers 847 and 2160 are coprime or not

Answer 1

its simple as that just apply Euclid's division algorithm on 847 and 2160 separately

Answer 2

coprimes are those whose HCF is 1 does we can use euclid's division algorithm to find out the HCF of 847 and 2160. if the HCF comes 1 then the numbers are coprime.
2160=847*2+466
847=466*1+381
466=381*1+85
361=85*4+21
85=21*4+1
21=1*21+0
therefore hcf(847,2160)=1
so yes the numbers are coprime