Why GCF matters
GCF is the number used to reduce fractions, simplify ratios and find the largest equal group size that divides several quantities.
Example
For 24, 36 and 60, the greatest common factor is 12 because 12 divides all three numbers and no larger positive integer does.
GCF vs LCM
Use GCF when simplifying or splitting into equal groups. Use least common multiple when finding a common denominator or when repeating cycles need to line up.
Common mistakes
Do not confuse common factors with common multiples. Factors divide into the numbers; multiples are produced by multiplying them.
Last reviewed: 2026-05-17