The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is:

Options

A. 48
B. 80
C. 96
D. 112

Answer

To find the other number when given the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers, we can use the relationship between these values. The relationship states that:

\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]

Given:
- HCF = 16
- LCM = 160
- Number 1 = 32
- Number 2 = x (the number we need to find)

### Step-by-step Solution:

1. **Write down the relationship**:
\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]
Substituting the known values:
\[ 16 \times 160 = 32 \times x \]

2. **Calculate the left side**:
\[ 16 \times 160 = 2560 \]
So, we have:
\[ 2560 = 32 \times x \]

3. **Isolate x**:
To find x, divide both sides by 32:
\[ x = \frac{2560}{32} \]

4. **Perform the division**:
\[ x = 80 \]

5. **Conclusion**:
The other number is 80.

### Final Answer:
The other number is **80**.