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Mathematics

The Euclidean Algorithm and Greatest Common Divisors

Quick fact

The Euclidean algorithm is one of the oldest algorithms still in use, dating back to ancient Greece (c. 300 BC). It can compute the GCD of two numbers without ever factoring them.

Why this is interesting

You've probably had to find the greatest common divisor of two numbers in school—like 12 and 18. But what if the numbers are 2,057,983 and 1,011, which is pretty hard to factor? The Euclidean algorithm finds the answer in just a few steps, and it’s been doing it for over 2,000 years.