The product of H.C.F. and L.C.M. of two numbers is 384. If one of them is 24, then other number is:

Options

A. 18
B. 6
C. 32
D. 16

Answer

To solve the problem, we need to find the other number when we know the product of the H.C.F. (Highest Common Factor) and L.C.M. (Lowest Common Multiple) of two numbers is 384, and one of the numbers is 24.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between H.C.F., L.C.M., and the two numbers can be expressed as:
\[ \text{H.C.F.} \times \text{L.C.M.} = \text{Product of the two numbers} \]
Let's denote the two numbers as \( a \) and \( b \). In this case, \( a = 24 \) and \( b \) is the unknown number.

2. **Set Up the Equation**:
According to the relationship, we can write:
\[ \text{H.C.F.} \times \text{L.C.M.} = 24 \times b \]
We know from the problem that:
\[ 24 \times b = 384 \]

3. **Solve for the Unknown Number**:
To find \( b \), we can rearrange the equation:
\[ b = \frac{384}{24} \]

4. **Perform the Division**:
Now, we need to calculate \( \frac{384}{24} \):
- First, divide 384 by 24.
- 24 goes into 384 exactly 16 times (since \( 24 \times 16 = 384 \)).

5. **Conclusion**:
Therefore, the other number \( b \) is:
\[ b = 16 \]

### Final Answer:
The other number is **16**.