The HCF of two numbers is 23 and their LCM is 1449 . If one of the numbers is 161 find the other .

Answer

To find the other number when the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two numbers are given, we can use the relationship:

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

Given:
- HCF = 23
- LCM = 1449
- One number (Number 1) = 161
- The other number (Number 2) = x (which 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:
\[ 23 \times 1449 = 161 \times x \]

2. **Calculate the left side**:
First, we need to calculate \(23 \times 1449\):
\[ 23 \times 1449 = 33227 \]

3. **Set up the equation**:
Now we can set up the equation:
\[ 33227 = 161 \times x \]

4. **Solve for x**:
To find x, we divide both sides by 161:
\[ x = \frac{33227}{161} \]

5. **Perform the division**:
Now, we calculate \(33227 \div 161\):
\[ x = 207 \]

### Conclusion:
The other number is **207**.