The largest positive integer that divides two or more integers without leaving a remainder. Also called the greatest common factor (GCF), it represents the largest number that is a factor of all given numbers.
The concept dates to ancient Greek mathematics, particularly Euclid's 'Elements' (circa 300 BCE), where the Euclidean algorithm for finding the GCD was first described. The English terminology developed as mathematical education became formalized in the 18th and 19th centuries.
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