Question

Using Euclid division algorithm, find which of the pairs of numbers are co-prime a) 231 , 396 b) 847, 2160

Answer 1

1) 396 , 231396=231 x 1 + 165
231=165 x 1 + 67
165=67 x 2 + 31
67=31 x 2 + 5
31=5 x 6 +1
5=1 x 5 + 0



2) 2160,8472160=847 x 2 +366
847=366 x 2 +115
366=115 x 2 +36
115=36 x 3 + 7
36=7 x 5 + 1
5=1 x 5 + 1


∴ these both are co-primes

Answer 2

Step-by-step explanation:

(i) 396 = 231 × 1 + 165 231 = 165 × 1 + 66 165 = 66 × 2 + 33 66 = 33 × 2 + 0. Therefore, HCF = 33. Hence, numbers are not co-prime. (ii) 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 Therefore, the HCF = 1. Hence, the numbers are co-prime.