What Is the Greatest Common Divisor?
Definition
Greatest Common Divisor: The largest positive whole number that divides two or more whole numbers without a remainder, also called the greatest common factor. The GCD of 84 and 126 is 42.
The greatest common divisor (GCD), also called the greatest common factor, is the largest whole number that divides two whole numbers without a remainder. The GCD of 84 and 126 is 42. To simplify a fraction, divide the numerator and the denominator by their GCD. A GCD of 1 means the fraction is already simplified.
Where it appears in the formulas
GCD = gcd(|numerator|, denominator). The fraction simplifier finds it with Euclid’s algorithm: 126 divided by 84 leaves 42, and 84 divided by 42 leaves 0, so the last divisor, 42, is the GCD. Then 84 / 42 = 2 and 126 / 42 = 3, and the fraction becomes 2/3.
How it differs from the LCM
The least common multiple (LCM) is the smallest positive whole number that is a multiple of both numbers. You use the GCD to simplify a fraction and the LCM to find a common denominator when you add fractions.