Computer Dictionary Online

Medical Dictionary Law Dictionary Legal Dictionary Website Design

0 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z

Euclid's Algorithm

<algorithm> (Or "Euclidean Algorithm") An algorithm for finding the greatest common divisor (GCD) of two numbers. It relies on the identity

		gcd(a, b) = gcd(a-b, b)

To find the GCD of two numbers by this algorithm, repeatedly replace the larger by subtracting the smaller from it until the two numbers are equal. E.g. 132, 168 -> 132, 36 -> 96, 36 -> 60, 36 -> 24, 36 -> 24, 12 -> 12, 12 so the GCD of 132 and 168 is 12.

This algorithm requires only subtraction and comparison operations but can take a number of steps proportional to the difference between the initial numbers (e.g. gcd(1, 1001) will take 1000 steps).

(1997-06-30)

Contact the Computer Dictionary Online :: Link to the Computer Dictionary Online :: Disclaimer for Computer Dictionary Online