Which of the following pair of numbers is relatively prime to each other?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (95, 112)
Two numbers are relatively prime (co-prime) when their only common factor is 1, that is, their HCF is 1. Each pair is broken into prime factors:
Option (1) (371, 159) — \(371=7\times53\) and \(159=3\times53\): 53 is common.
Option (2) (407, 259) — \(407=11\times37\) and \(259=7\times37\): 37 is common.
Option (3) (95, 112) — \(95=5\times19\) and \(112=2^4\times7\): no common prime factor, so the HCF is 1 and the pair is co-prime.
Option (4) (57, 123) — \(57=3\times19\) and \(123=3\times41\): 3 is common.
Tip: Split the easier number of the pair into primes and test only those primes on the other number: 95 is \(5\times19\), and 112 is divisible by neither 5 nor 19, so the pair is co-prime.