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Finding the Greatest Common Divisor of Two Numbers by Factoring

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You can find the greatest common divisor (GCD) of two numbers by multiplying together all the prime factors they have in common.

Contributed by: Jesse Nochella (March 2011)
Open content licensed under CC BY-NC-SA

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A much more efficient way of computing GCDs has been known for the past 2300 years. Named the Euclidean Algorithm, it is one of the oldest mathematical procedures known, appearing in Euclid's Elements around 300 BC.

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