You are here: irt.org | FOLDOC | 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)
Nearby terms: Euclid « Euclidean Algorithm « Euclidean norm « Euclid's Algorithm » Eudora » EULA » EULER
FOLDOC, Topics, 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, ?, ALL