# euclid's algorithm

Computing Dictionary

### Euclid's Algorithm definition

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)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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