How the gCF Calculator works
The greatest common factor is the largest whole number dividing every number in your list, found here with the Euclidean algorithm: repeatedly replace the larger number with the remainder until it hits zero. The LCM comes free from the identity a × b = GCF × LCM.
GCF(a, b): repeat a, b → b, a mod b until b = 0 | LCM = a × b ÷ GCF
Example: for 24, 36, and 60 the GCF is 12 and the LCM is 360, which is why 12 is the biggest tile that measures all three lengths evenly.
Frequently asked questions
What is the GCF used for?
Simplifying fractions (divide top and bottom by their GCF), splitting things into the largest equal groups, and finding the biggest square tile that fits a floor exactly.
What if the GCF is 1?
The numbers are coprime, sharing no factors. Any fraction between them is already in lowest terms.
GCF vs LCM in one sentence?
GCF is the largest number that divides into all of them, LCM is the smallest number they all divide into. Fraction simplification uses GCF, common denominators use LCM.