The highest common factor and least common multiple of two numbers are 35 and 525 respectively. If one of them has 175, then other number is

Options

A. 75
B. 85
C. 95
D. 105

Answer

To solve the problem, we need to find the other number when one of the numbers is given as 175, and we know the highest common factor (HCF) and least common multiple (LCM) of the two numbers.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- HCF (Highest Common Factor) = 35
- LCM (Least Common Multiple) = 525
- One number (let's call it A) = 175

2. **Let the Other Number be X:**
- We need to find the value of X.

3. **Use the Relationship Between HCF, LCM, and the Two Numbers:**
- The relationship states that:
\[ \text{HCF} \times \text{LCM} = A \times X \]
- Substituting the known values into the equation:
\[ 35 \times 525 = 175 \times X \]

4. **Calculate the Left Side:**
- First, calculate \( 35 \times 525 \):
\[ 35 \times 525 = 18375 \]

5. **Set Up the Equation:**
- Now we have:
\[ 18375 = 175 \times X \]

6. **Solve for X:**
- To find X, divide both sides by 175:
\[ X = \frac{18375}{175} \]

7. **Perform the Division:**
- Calculate \( \frac{18375}{175} \):
\[ X = 105 \]

8. **Conclusion:**
- The other number is \( X = 105 \).

### Final Answer:
The other number is **105**.