Which of the following is a pair of co-primes ?

Options

A. (14,35)
B. (18,25)
C. (31,93)
D. (32,62)

Answer

To determine which of the given pairs is a pair of co-prime numbers, we need to follow these steps:

### Step-by-Step Solution:

1. **Understand Co-prime Numbers**: Co-prime numbers are two numbers that have no common factors other than 1. This means their highest common factor (HCF) is 1.

2. **Evaluate Each Pair**: We will evaluate each pair of numbers given in the options to check if they are co-prime.

3. **Check Pair 1: 14 and 35**:
- **Factors of 14**: 1, 2, 7, 14
- **Factors of 35**: 1, 5, 7, 35
- **Common Factors**: 1, 7
- **Conclusion**: HCF(14, 35) = 7, so they are not co-prime.

4. **Check Pair 2: 18 and 25**:
- **Factors of 18**: 1, 2, 3, 6, 9, 18
- **Factors of 25**: 1, 5, 25
- **Common Factors**: 1
- **Conclusion**: HCF(18, 25) = 1, so they are co-prime.

5. **Check Pair 3: 31 and 93**:
- **Factors of 31**: 1, 31
- **Factors of 93**: 1, 3, 31, 93
- **Common Factors**: 1, 31
- **Conclusion**: HCF(31, 93) = 31, so they are not co-prime.

6. **Check Pair 4: 32 and 62**:
- **Factors of 32**: 1, 2, 4, 8, 16, 32
- **Factors of 62**: 1, 2, 31, 62
- **Common Factors**: 1, 2
- **Conclusion**: HCF(32, 62) = 2, so they are not co-prime.

7. **Final Conclusion**: The only pair that is co-prime is **18 and 25**.

### Answer:
The pair of co-prime numbers is **18 and 25**.

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