Which of the following is a pair of coprime numbers ?

Question

Accepted Answer

Option 2, which is the pair (17, 25), is the correct answer because these two numbers are coprime. Coprime numbers, also known as relatively prime numbers, are two numbers that have no common factors other than 1. In other words, their greatest common divisor (GCD) is 1.

1. **Explanation for Option 2 (17, 25):**
   - The number 17 is a prime number, meaning its only divisors are 1 and 17.
   - The number 25 is not a prime number; it is a perfect square with divisors 1, 5, and 25.
   - The only common divisor between 17 and 25 is 1, which makes them coprime.

2. **Explanation for why other options are incorrect:**

- **Option 1 (7, 49):**
     - The number 49 is a multiple of 7 (since 49 = 7 × 7).
     - Therefore, the common divisors of 7 and 49 are 1 and 7, making them not coprime.

- **Option 3 (8, 52):**
     - The number 8 has divisors 1, 2, 4, and 8.
     - The number 52 has divisors 1, 2, 4, 13, 26, and 52.
     - The common divisors of 8 and 52 are 1, 2, and 4, which means they are not coprime.

- **Option 4 (13, 91):**
     - The number 13 is a prime number.
     - The number 91 can be factored into 7 and 13 (since 91 = 7 × 13).
     - The common divisor of 13 and 91 is 13, making them not coprime.

In conclusion, Option 2 (17, 25) is the only pair where the greatest common divisor is 1, confirming that they are coprime numbers.