The largest positive integer that divides two or more integers without leaving a remainder, also known as the greatest common divisor (GCD). It's used to reduce fractions to their simplest form.
From Latin 'factor' meaning 'maker' or 'doer' and 'communis' meaning 'shared'. Euclid described the algorithm for finding the GCD around 300 BCE in his Elements, making it one of the oldest known algorithms still in use today.
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