The HCF of `5^(13) and 2^(26)` is

Options

A. 0
B. 1
C. 13
D. 26

Answer

To find the HCF (Highest Common Factor) of \(5^{13}\) and \(2^{26}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: We have two numbers, \(5^{13}\) and \(2^{26}\).

2. **Determine the Prime Factorization**:
- The prime factorization of \(5^{13}\) is simply \(5^{13}\) (since 5 is a prime number).
- The prime factorization of \(2^{26}\) is \(2^{26}\) (since 2 is also a prime number).

3. **Check for Common Factors**:
- The prime factors of \(5^{13}\) are only 5.
- The prime factors of \(2^{26}\) are only 2.
- Since 5 and 2 are different prime numbers, they have no common factors.

4. **Conclusion**:
- The only common factor between \(5^{13}\) and \(2^{26}\) is 1.
- Therefore, the HCF (or SCF) of \(5^{13}\) and \(2^{26}\) is **1**.

### Final Answer:
The HCF of \(5^{13}\) and \(2^{26}\) is **1**.