Explanation:

Let’s break it down, option by option:

- Option 1: 51, 63

Both are divisible by 3. So, they’re not co-prime.

- Option 2: 52, 91

52 factors into 2 × 2 × 13, and 91 factors into 7 × 13.

Both share a 13, so they’re not co-prime either.

- Option 3: 71, 81

71 is a prime number. 81 is 34. They share no common factors except 1.

These two are co-prime.

- Option 4: 81, 99

Both divisible by 9 and 3. So, nope—definitely not co-prime.

So, the answer is Option 3: 71, 81.