Translation

powered by

Computing (FOLDOC) dictionary

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).