The pair of number which are relatively prime to each other is

Options

A. (68,85)
B. (65,91)
C. (92,85)
D. (102,153)

Answer

To determine which pair of numbers is relatively prime to each other, we need to find the highest common factor (HCF) of each pair. Two numbers are considered relatively prime if their HCF is 1.

Let’s analyze the given options step by step:

### Step 1: Analyze the first pair (68 and 85)
1. **Find the HCF of 68 and 85**:
- Prime factorization of 68:
- 68 = 2 × 34 = 2 × 2 × 17 = 2² × 17
- Prime factorization of 85:
- 85 = 5 × 17
- Common factor: 17
- HCF(68, 85) = 17

### Step 2: Analyze the second pair (65 and 91)
2. **Find the HCF of 65 and 91**:
- Prime factorization of 65:
- 65 = 5 × 13
- Prime factorization of 91:
- 91 = 7 × 13
- Common factor: 13
- HCF(65, 91) = 13

### Step 3: Analyze the third pair (92 and 85)
3. **Find the HCF of 92 and 85**:
- Prime factorization of 92:
- 92 = 2 × 46 = 2 × 2 × 23 = 2² × 23
- Prime factorization of 85:
- 85 = 5 × 17
- No common factors
- HCF(92, 85) = 1

### Step 4: Analyze the fourth pair (102 and 153)
4. **Find the HCF of 102 and 153**:
- Prime factorization of 102:
- 102 = 2 × 51 = 2 × 3 × 17
- Prime factorization of 153:
- 153 = 3 × 51 = 3 × 3 × 17
- Common factor: 51
- HCF(102, 153) = 51

### Conclusion
After analyzing all pairs:
- HCF(68, 85) = 17 (not relatively prime)
- HCF(65, 91) = 13 (not relatively prime)
- HCF(92, 85) = 1 (relatively prime)
- HCF(102, 153) = 51 (not relatively prime)

Thus, the pair of numbers that are relatively prime to each other is **92 and 85**.