If the product of two numbers is 3360 and their LCM is 96, then their HCF is:

Options

A. 35
B. 33
C. 34
D. 29

Answer

To solve the problem, we need to find the HCF (Highest Common Factor) of two numbers given their product and LCM (Least Common Multiple). The relationship between the product of two numbers, their HCF, and their LCM is given by the formula:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Product of the two numbers = 3360
- LCM of the two numbers = 96

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

3. **Substitute the values into the formula**:
\[ \text{HCF} = \frac{3360}{96} \]

4. **Perform the division**:
- First, simplify \(3360 \div 96\).
- To do this, we can divide 3360 by 96 directly:
- 96 goes into 3360. We can estimate how many times it goes.
- \(96 \times 3 = 288\) (which is less than 336)
- \(96 \times 4 = 384\) (which is more than 336)
- So, we try \(96 \times 35\) (as we can check for larger multipliers).
- \(96 \times 35 = 3360\).

5. **Calculate the HCF**:
\[ \text{HCF} = 35 \]

### Final Answer:
The HCF of the two numbers is **35**.