meaning of euclids

1. Euclids Algorithm Or "Euclidean Algorithm" An algorithm for finding the greatest common divisor GCD of two numbers. It relies on the identity gcda, b = gcda-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. gcd1, 1001 will take 1000 steps.

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