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The GCD of two integers X and Y is the largest integer that divides both of X and Y (without leaving a remainder). Greatest Common Divisor is, also, known as greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm) and highest common divisor.

This is a companion discussion topic for the original entry at http://iq.opengenus.org/euclidean-algorithm-greatest-common-divisor-gcd/