If the product of two numbers is 2400 and their LCM is 96 then their HCF is.

Options

A. 35
B. 240
C. 24
D. 25

Answer

To find the HCF (Highest Common Factor) of two numbers when their product and LCM (Least Common Multiple) are given, we can use the relationship:

\[ \text{Product of two numbers} = \text{LCM} \times \text{HCF} \]

Given:
- Product of two numbers = 2400
- LCM = 96

We need to find the HCF.

### Step-by-Step Solution:

1. **Use the relationship**:
\[ \text{HCF} = \frac{\text{Product of two numbers}}{\text{LCM}} \]

2. **Substitute the known values**:
\[ \text{HCF} = \frac{2400}{96} \]

3. **Perform the division**:
- First, simplify the fraction:
\[ \text{HCF} = \frac{2400 \div 96}{1} = \frac{2400}{96} \]

4. **Cancel out common factors**:
- To simplify \( \frac{2400}{96} \), we can divide both the numerator and denominator by 16 (since 16 is a common factor):
\[ \frac{2400 \div 16}{96 \div 16} = \frac{150}{6} \]

5. **Continue simplifying**:
- Now divide 150 by 6:
\[ 150 \div 6 = 25 \]

6. **Conclusion**:
\[ \text{HCF} = 25 \]

### Final Answer:
The HCF of the two numbers is **25**.