The Euclidean Algorithm

The Euclidean Algorithm is a method for finding the greatest common divisor (GCD) of two numbers—that is, the largest number that divides both without leaving a remainder. It works by repeatedly dividing the larger number by the smaller and replacing the larger with the smaller and the smaller with the remainder from the division. This process continues until the remainder is zero. The last non-zero remainder is the GCD. It's an efficient way to determine what large numbers share as their biggest common factor, useful in simplifying fractions and solving related problems.