If the product of two numbers is 3192 and their LCM is 56 then their HCF is :
A. 58
B. 59
C. 56
D. 57

Options

A. C
B. A
C. B
D. D

Answer

To find the HCF (Highest Common Factor) of two numbers when given their product and LCM (Least Common Multiple), we can use the relationship between these quantities. The formula we will use is:

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

Given:
- Product of the two numbers = 3192
- LCM = 56

We need to find the HCF. Let's denote HCF as \( x \).

Using the formula, we can set up the equation:

\[ 3192 = 56 \times x \]

Now, we can solve for \( x \):

1. **Step 1: Rearranging the equation**
\[ x = \frac{3192}{56} \]

2. **Step 2: Performing the division**
To divide 3192 by 56, we can simplify it step by step:
- First, we can simplify the division by breaking it down.
- 56 goes into 3192. We can estimate how many times it fits.
- 56 fits into 3192 approximately 57 times (since \( 56 \times 57 = 3192 \)).

Thus, we find:
\[ x = 57 \]

So, the HCF of the two numbers is **57**.

### Final Answer:
The HCF is **57**, which corresponds to option D.