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In page Greatest common divisor:
"The computational complexity of the computation of greatest common divisors has been widely studied.[1] If one uses the Euclidean algorithm and the elementary algorithms for multiplication and division, the computation of the greatest common divisor of two integers of at most n bits is O(n2).[citation needed] This means that the computation of greatest common divisor has, up to a constant factor, the same complexity as the multiplication.
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