GCF Calculator
Greatest common factor (also called greatest common divisor) of any list of whole numbers — with prime factorization and the Euclidean algorithm shown step by step.
What is the greatest common factor?
The greatest common factor (GCF) — also called the greatest common divisor (GCD) — of a set of positive integers is the largest whole number that divides every one of them evenly. If the only shared factor is 1, the numbers are called coprime. GCF is the tool for reducing fractions, simplifying ratios, and splitting quantities into the largest possible equal groups.
GCF calculator, piece by piece
This calculator reports the GCF using two independent methods so you can check your working either way. Each card explains one part of what appears in the output above.
Prime factorization — the intuitive method
The calculator factors every input, then for each prime that appears in every factorization it takes the lowestpower. Multiplying those together gives the GCF — the Venn diagram above shows exactly which primes made it into the overlap.
Euclidean algorithm — no factoring required
For two-number inputs the calculator also shows the Euclidean algorithm: divide, keep the remainder, repeat until the remainder is zero. The last non-zero remainder is the GCF, and this method stays fast even when the inputs would be painful to factor by hand.
Three or more numbers — pairwise folding
When you enter three or more values the calculator folds the two-input GCF across the list: GCF of the first pair, then GCF of that result with the next number, and so on. Order does not affect the answer, so you can throw in as many inputs as you need.
Features of this calculator
- Accepts a comma- or space-separated list of two or more positive integers
- Shows the prime factorization of every input and calls out the shared primes
- Displays the Euclidean algorithm side by side for two-number inputs
- Handles large numbers without overflow
- Pairs naturally with the LCM calculator on the same values
Frequently asked questions
+Is GCF the same as GCD?
Yes — "greatest common factor" and "greatest common divisor" are two names for the same number.
+What is the fastest way to find the GCF of large numbers?
Use the Euclidean algorithm. It reaches the answer in a handful of divisions even when the inputs are in the millions, whereas prime factorization becomes impractical once the numbers get large.
+What is the GCF of two coprime numbers?
Always 1 — that is the definition of coprime.
+Why can't I enter 0?
Every integer divides 0 evenly, so the GCF of only zeros is undefined. Formally gcd(a, 0) = |a| when a ≠ 0, but this calculator asks for positive integers to keep the inputs unambiguous.