The largest positive integer that divides two or more integers without leaving a remainder. Also known as the greatest common factor (GCF), it represents the highest number that is a factor of all given numbers.
From Old English 'great' meaning 'large', Latin 'communis' meaning 'shared', and 'dividere' meaning 'to separate'. The concept dates back to Euclid's Elements (300 BCE), where the Euclidean algorithm for finding the GCD was first systematically described.
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