The Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two integers. It works by repeatedly subtracting the smaller number from the larger one or using division to find remainders until one of the numbers becomes zero. The last non-zero remainder is the GCD. This algorithm is efficient and can be applied to any pair of integers, regardless of their size. It is named after the ancient Greek mathematician Euclid, who first described it in his work, Elements. The algorithm is fundamental in number theory and has applications in various fields, including cryptography.