The Greatest Common Factor (GCF), also called Greatest Common Divisor (GCD), is the largest integer that divides two or more numbers exactly. Used in simplifying fractions, finding common denominators, and solving Diophantine equations.
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Pro Tip
To simplify a fraction: divide numerator and denominator by their GCF. 48/18 → GCF=6 → 8/3 (fully simplified).
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Did You Know?
The Euclidean algorithm (300 BCE) is one of the oldest algorithms still in use — over 2,300 years old. It is used in modern cryptography (RSA) to find modular inverses.
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