The product of two number is 1680 and the LCM of two number is 420. Find their HCF.

Explanation

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

**LCM × HCF = Product of the two numbers**

Given:
- Product of the two numbers = 1680
- LCM of the two numbers = 420

We need to find the HCF.

### Step-by-Step Solution:

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

2. **Substitute the known values**:
Substitute the values we have into the equation:
\[ 420 \times \text{HCF} = 1680 \]

3. **Solve for HCF**:
To find the HCF, we can rearrange the equation:
\[ \text{HCF} = \frac{1680}{420} \]

4. **Calculate the division**:
Now, perform the division:
\[ \text{HCF} = \frac{1680}{420} = 4 \]

5. **Conclusion**:
Therefore, the HCF of the two numbers is:
\[ \text{HCF} = 4 \]