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.
The greatest common divisor is mathematics' ultimate matchmaker - it finds the biggest number that all your given numbers can 'agree on' as a common factor! It's the key to simplifying fractions, solving Diophantine equations, and even securing your credit card transactions through cryptography.
Complete word intelligence in one call. Free tier — 50 lookups/day.