H.C.F. of two numbers =

Options

A. Product of two numbers + their L.C.M.
B. Product of two numbers - their L.C.M.
C. Product of two numbers `xx` their L.C.M.
D. Product of two numbers `div` their L.C.M.

Answer

To find the H.C.F. (Highest Common Factor) of two numbers using the relationship between H.C.F., L.C.M. (Lowest Common Multiple), and the product of the two numbers, follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
We know that the relationship between H.C.F., L.C.M., and the product of two numbers is given by the formula:
\[ \text{H.C.F.}(a, b) \times \text{L.C.M.}(a, b) = a \times b \]

2. **Rearranging the Formula**:
To find the H.C.F., we can rearrange the formula:
\[ \text{H.C.F.}(a, b) = \frac{a \times b}{\text{L.C.M.}(a, b)} \]

3. **Identify the Options**:
From the question, we have four options:
- Option 1: Product of two numbers + their LCM
- Option 2: Product of two numbers - their LCM
- Option 3: Product of two numbers × their LCM
- Option 4: Product of two numbers ÷ their LCM

4. **Select the Correct Option**:
According to our rearranged formula, the H.C.F. of two numbers is equal to the product of the two numbers divided by their L.C.M. Therefore, the correct option is:
\[ \text{Option 4: Product of two numbers ÷ their LCM} \]

### Final Answer:
The H.C.F. of two numbers is equal to the product of the two numbers divided by their L.C.M.

---