The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is:

Options

A. 147
B. 528
C. 132
D. 264

Answer

To find the second number given the HCF, LCM, and the first number, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- HCF (Highest Common Factor) = 44
- LCM (Lowest Common Multiple) = 264
- When the first number is divided by 2, the quotient is 44.

2. **Calculate the First Number:**
- Let the first number be \( N_1 \).
- According to the problem, when \( N_1 \) is divided by 2, the quotient is 44.
- Therefore, we can express this as:
\[ N_1 = 2 \times 44 = 88 \]

3. **Use the Relationship Between HCF, LCM, and the Two Numbers:**
- The relationship states that:
\[ \text{HCF} \times \text{LCM} = N_1 \times N_2 \]
- Substituting the known values:
\[ 44 \times 264 = 88 \times N_2 \]

4. **Calculate the Product of HCF and LCM:**
- First, calculate \( 44 \times 264 \):
\[ 44 \times 264 = 11616 \]

5. **Set Up the Equation:**
- Now we have:
\[ 11616 = 88 \times N_2 \]

6. **Solve for the Second Number \( N_2 \):**
- To find \( N_2 \), divide both sides by 88:
\[ N_2 = \frac{11616}{88} \]
- Performing the division:
\[ N_2 = 132 \]

7. **Conclusion:**
- The other number is \( N_2 = 132 \).

### Final Answer:
The other number is **132**.