GCD Calculator
Understanding the GCD
The Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF), of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.
Euclidean Algorithm
The most efficient method for finding the GCD of two numbers is the Euclidean algorithm. For two integers 'a' and 'b', the GCD is found by repeatedly applying the division algorithm.
\[ \text{gcd}(a, b) = \text{gcd}(b, a \pmod b) \]
This process is repeated until the remainder is 0. The last non-zero remainder is the GCD. To find the GCD of a list of numbers, you find the GCD of the first two, then the GCD of that result and the next number, and so on.
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