To determine which of the pairs is co-prime, we need to check the greatest common divisor (GCD) of each pair. Two numbers are co-prime if their GCD is 1.
Let's analyze each pair:
a) 51, 63
- Factors of 51: 1, 3, 17, 51
- Factors of 63: 1, 3, 7, 9, 21, 63
- Common factors: 1, 3
- GCD: 3 (not co-prime)
b) 52, 91
- Factors of 52: 1, 2, 4, 13, 26, 52
- Factors of 91: 1, 7, 13, 91
- Common factors: 1, 13
- GCD: 13 (not co-prime)
c) 71, 81
- Factors of 71: 1, 71
- Factors of 81: 1, 3, 9, 27, 81
- Common factors: 1
- GCD: 1 (co-prime)
d) 81, 99
- Factors of 81: 1, 3, 9, 27, 81
- Factors of 99: 1, 3, 9, 11, 33, 99
- Common factors: 1, 3, 9
- GCD: 9 (not co-prime)
Therefore, the pair that is co-prime is:
c) 71, 81
