Question

Which one is a pair of co-prime numbers?

• A. (18, 25)
• B. (5, 15)
• C. (7, 21)
• D. (31, 93)

Hint:

Two numbers are co-prime if their greatest common divisor (GCD) is 1.

Answer 1

The Correct Option is A

Step 1: Definition of co-prime numbers.
Two numbers are said to be co-prime if their greatest common divisor (GCD) is 1. We need to check the GCD of each pair to determine which one is co-prime.
Step 2: Check GCD of each pair.
- GCD of 18 and 25: The factors of 18 are \( 1, 2, 3, 6, 9, 18 \) and the factors of 25 are \( 1, 5, 25 \). The common factor is \( 1 \), so 18 and 25 are co-prime.
- GCD of 5 and 15: The factors of 5 are \( 1, 5 \) and the factors of 15 are \( 1, 3, 5, 15 \). The common factor is \( 5 \), so 5 and 15 are not co-prime.
- GCD of 7 and 21: The factors of 7 are \( 1, 7 \) and the factors of 21 are \( 1, 3, 7, 21 \). The common factor is \( 7 \), so 7 and 21 are not co-prime.
- GCD of 31 and 93: The factors of 31 are \( 1, 31 \) and the factors of 93 are \( 1, 3, 31, 93 \). The common factor is \( 31 \), so 31 and 93 are not co-prime.

Step 3: Conclusion.
Only the pair (18, 25) has a GCD of 1, meaning they are co-prime. Hence, the correct answer is (A).