The product of two numbers is 2560 and their LCM is 320 . Find their HCF.

Options

A. 7
B. 8
C. 9
D. 10

Answer

To find the HCF (Highest Common Factor) of two numbers when the product of the numbers and their LCM (Least Common Multiple) is given, we can use the relationship between these three values. The formula we will use is:

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

Given:
- Product of the two numbers = 2560
- LCM of the two numbers = 320

We need to find the HCF.

### Step-by-Step Solution:

1. **Write down the formula**:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

2. **Substitute the known values into the formula**:
\[ \text{HCF} \times 320 = 2560 \]

3. **Rearrange the formula to solve for HCF**:
\[ \text{HCF} = \frac{2560}{320} \]

4. **Perform the division**:
- First, simplify the fraction:
\[ \frac{2560}{320} = \frac{2560 \div 320}{320 \div 320} = \frac{8}{1} = 8 \]

5. **Conclusion**:
The HCF of the two numbers is **8**.