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

Answer

To find the HCF of two numbers given their LCM and product, we can use the relationship between HCF, LCM, and the product of the two numbers. The formula is:

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

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

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:**
\[ \text{HCF} \times 192 = 3072 \]

3. **Rearrange the equation to solve for HCF:**
\[ \text{HCF} = \frac{3072}{192} \]

4. **Perform the division:**
- First, simplify \( \frac{3072}{192} \).
- Divide both numbers by 16 to make calculations easier:
\[ 3072 \div 16 = 192 \quad \text{and} \quad 192 \div 16 = 12 \]
- Now, divide:
\[ \frac{192}{12} = 16 \]

5. **Conclusion:**
\[ \text{HCF} = 16 \]

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