A tool employing the Euclidean algorithm determines the greatest common divisor (GCD) of two integers. For example, given the numbers 56 and 70, such a tool would systematically determine their GCD to be 14. It operates by repeatedly applying the division algorithm, subtracting the smaller number from the larger until one of the numbers becomes zero. The last non-zero remainder is the GCD.
This method offers an efficient pathway to finding the GCD, a fundamental concept in number theory with wide-ranging applications in fields like cryptography and computer science. Dating back to ancient Greece, its longevity speaks to its fundamental importance in mathematics. This foundational algorithm underpins various modern computational processes.
