Identify a pair of co-primes (gcd equals 1) From the given pairs, select the pair whose greatest common divisor is exactly 1.

Introduction / Context:
Two integers are co-prime if their only common positive divisor is 1. This is equivalent to saying their gcd (HCF) is 1. We check each pair quickly using small prime factors.

Given Data / Assumptions:

• Pairs: (14, 35), (18, 25), (31, 93), (32, 62), (21, 28).
• Co-prime ⇔ gcd = 1.

Concept / Approach:
Factor each pair lightly: look for obvious shared primes such as 2, 3, 5, 7, 11, 31.

Step-by-Step Solution:
(14, 35): 14 = 2 * 7, 35 = 5 * 7 ⇒ gcd ≥ 7 ⇒ not co-prime.(18, 25): 18 = 2 * 3^2, 25 = 5^2 ⇒ no common primes ⇒ gcd = 1 ⇒ co-prime.(31, 93): 93 = 3 * 31 ⇒ gcd ≥ 31 ⇒ not co-prime.(32, 62): 32 = 2^5, 62 = 2 * 31 ⇒ gcd ≥ 2 ⇒ not co-prime.(21, 28): 21 = 3 * 7, 28 = 4 * 7 ⇒ gcd ≥ 7 ⇒ not co-prime.

Verification / Alternative check:
Euclidean algorithm on (18, 25): 25 mod 18 = 7, 18 mod 7 = 4, 7 mod 4 = 3, 4 mod 3 = 1 ⇒ gcd = 1.

Why Other Options Are Wrong:
Each has a clear shared factor (7, 31, 2, or 7 respectively), so gcd is greater than 1.

Common Pitfalls:
Assuming numbers with different parity must be co-prime (not always), or overlooking large shared primes like 31.

Final Answer:
(18, 25)