The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two numbers is the largest positive integer that divides both numbers without leaving a remainder.

To find the HCF of 26 and 455, we can use the Euclidean Algorithm. This method involves repeatedly applying the division algorithm: we divide the larger number by the smaller number, then take the divisor and divide it by the remainder from the previous step. We continue this process until the remainder is zero. The divisor at this final step is the HCF.

Step 1: Divide 455 (the larger number) by 26 (the smaller number).

$455 = 26 \times 17 + 13$

Here, the quotient is 17 and the remainder is 13.

Step 2: Now, take the previous divisor (26) and divide it by the remainder from Step 1 (13).

$26 = 13 \times 2 + 0$

The remainder is now 0.

Since the remainder has become zero, the divisor at this step, which is $13$ , is the HCF of 26 and 455.

Final Answer: The HCF of 26 and 455 is $13$ .

Related Topics and Formulae

Prime Factorization Method: Another common method for finding the HCF is by finding the prime factors of each number.

Prime factors of 26: $2 \times 13$

Prime factors of 455: $5 \times 7 \times 13$

The common prime factor is $13$ . Therefore, HCF = 13.

Formula connecting HCF and LCM: For any two numbers, a and b:

$HCF (a, b) \times LCM (a, b) = a \times b$