The LCM of two number is 192 and their product is 3072. Find the HCF of two numbers.

Answer

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

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

Given:
- LCM = 192
- Product of the two numbers = 3072

Let's denote the HCF as \( H \).

### Step-by-Step Solution:

1. **Write down the relationship**:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]
This can be expressed as:
\[ 192 \times H = 3072 \]

2. **Rearrange the equation to find H**:
\[ H = \frac{3072}{192} \]

3. **Perform the division**:
- First, simplify \( \frac{3072}{192} \).
- To do this, we can perform the division directly:
\[ 3072 \div 192 = 16 \]

4. **Conclusion**:
The HCF of the two numbers is:
\[ H = 16 \]

### Final Answer:
The HCF of the two numbers is **16**.