How to find the GCF
The greatest common factor is the largest number that divides evenly into all of your numbers. A quick method is the Euclidean algorithm:
GCF(a, b) = GCF(b, a mod b), until the remainder is 0
For 24 and 36: 36 mod 24 = 12, then 24 mod 12 = 0, so the GCF is 12. For three or more numbers, take the GCF of the first two, then combine it with the next, and so on.
Simplifying fractions with the GCF
The GCF's most common job is reducing fractions. Divide the top and bottom by their GCF to get the lowest terms. Since GCF(18, 24) = 6, the fraction 18/24 simplifies to 3/4.
GCF and LCM together
For any two numbers, the GCF and the least common multiple multiply to the same thing as the two numbers themselves:
GCF(a, b) × LCM(a, b) = a × b
Frequently asked questions
What is the greatest common factor (GCF)?
The GCF of two or more whole numbers is the largest number that divides all of them with no remainder. For 24 and 36, the common factors are 1, 2, 3, 4, 6, and 12 — so the GCF is 12. It is also called the greatest common divisor (GCD).
How do you find the GCF?
One reliable way is the Euclidean algorithm: divide the larger number by the smaller, then replace the larger with the remainder and repeat until the remainder is zero — the last non-zero divisor is the GCF. For more than two numbers, find the GCF of the first two, then of that result and the next number, and so on. This calculator does it instantly.
What is the GCF used for?
The most common use is simplifying fractions: divide the numerator and denominator by their GCF to reduce the fraction to lowest terms. The GCF also helps when splitting things into equal groups or finding the largest tile that fits a space evenly.
What is the difference between GCF and LCM?
The GCF is the largest number that divides all your values, while the least common multiple (LCM) is the smallest number all your values divide into. They are related: for two numbers, GCF × LCM = the product of the two numbers. This calculator shows both.
Tip: The GCF is defined for whole numbers — decimals and fractions are rounded to the nearest whole number before the calculation.