Given that LCM (26, 169) = 338, find HCF (26, 169).

Answer

To find the HCF (Highest Common Factor) of the numbers 26 and 169 given that their LCM (Lowest Common Multiple) is 338, we can use the relationship between LCM, HCF, and the product of the two numbers.

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between HCF, LCM, and the product of two numbers is given by the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

2. **Identify the known values**:
- LCM(26, 169) = 338
- The two numbers are 26 and 169.

3. **Calculate the product of the two numbers**:
\[ \text{Product} = 26 \times 169 \]

4. **Perform the multiplication**:
\[ 26 \times 169 = 4394 \]

5. **Set up the equation using the relationship**:
\[ \text{HCF} \times 338 = 4394 \]

6. **Solve for HCF**:
\[ \text{HCF} = \frac{4394}{338} \]

7. **Perform the division**:
- First, simplify the fraction:
\[ \text{HCF} = \frac{4394 \div 169}{338 \div 169} = \frac{26}{2} = 13 \]

8. **Conclusion**:
Hence, the HCF of 26 and 169 is:
\[ \text{HCF} = 13 \]