Find the HCF of 26 and 455.

Answer

To find the HCF (Highest Common Factor) of 26 and 455, we can use the prime factorization method. Here’s a step-by-step solution:

### Step 1: Prime Factorization of 26
- Start by finding the prime factors of 26.
- 26 is an even number, so we can divide it by 2.
- \( 26 \div 2 = 13 \)
- Now, we check if 13 is a prime number. Since 13 has no divisors other than 1 and itself, it is prime.
- Therefore, the prime factorization of 26 is:
\[ 26 = 2 \times 13 \]

### Step 2: Prime Factorization of 455
- Next, we find the prime factors of 455.
- First, check if 455 is divisible by 5 (it ends in 5).
- \( 455 \div 5 = 91 \)
- Now, we need to factor 91. We check for divisibility by 7:
- \( 91 \div 7 = 13 \)
- Since 13 is a prime number, we stop here.
- Therefore, the prime factorization of 455 is:
\[ 455 = 5 \times 7 \times 13 \]

### Step 3: Identify Common Factors
- Now, we compare the prime factorizations of both numbers:
- \( 26 = 2 \times 13 \)
- \( 455 = 5 \times 7 \times 13 \)
- The common prime factor between the two numbers is 13.

### Step 4: Conclusion
- The HCF of 26 and 455 is the highest common factor we found, which is:
\[ \text{HCF} = 13 \]

### Summary
Thus, the HCF of 26 and 455 is **13**.

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