Greatest Common Divisor (Greatest Common Divisor)
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Description
Let $a_1, \ldots, a_m$ be given nonzero integers. Then $g$ is called the greatest common divisor (GCD) of $a_1, \ldots, a_m$ if and only if it is the largest integer that divides all $a_1, \ldots, a_m$.
Parameters
$n$: sum of number of bits among the integers
Table of Algorithms
Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|
Euclid's algorithm | -300 | $O(n^{2})$ | $O(n)$ | Exact | Deterministic | |
Lehmer's GCD algorithm | 1940 | $O(n^{2})$ | $O(n)$ | Exact | Deterministic | |
Binary GCD algorithm | 1967 | $O(n^{2})$ | $O(n)$ | Exact | Deterministic | Time |
Sthele, Zimmermann | 2006 | $O(n \log^{2} n \log \log n)$ | $O(n)$?? | Exact | Deterministic | Time |
Time Complexity Graph
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