CalcaTools

GCF Calculator

A GCF calculator finds the greatest common factor — the largest number that divides them all — of two or more whole numbers.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

NumbersGCF
12, 186
24, 3612
8, 91 (coprime)
48, 60, 7212

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

MethodBest for
List factorsSmall numbers
Prime factorizationMedium numbers; shared primes
Euclidean algorithmLarge numbers — fastest
GCF = 1Numbers are coprime

Formula & methodology

Formula: GCF(a, b) = product of the lowest power of each shared prime; Euclid: GCF(a,b) = GCF(b, a mod b)

How the greatest common factor is found

The GCF (also called GCD) is the largest number that divides every input with no remainder.

Prime factorization

12 = 2^2 x 3 and 18 = 2 x 3^2. Shared primes are 2 and 3 at their lowest powers: 2^1 x 3^1 = 6.

Euclidean algorithm (fast)

GCF(48, 60): 60 mod 48 = 12; 48 mod 12 = 0, so GCF = 12. Repeatedly replace the pair with (smaller, remainder) until the remainder is 0.

If the GCF is 1, the numbers share no common factor and are called coprime.

Frequently asked questions

How do you find the greatest common factor?
List the factors of each number and take the largest they share, or use prime factorization: write each number as a product of primes and multiply the primes they have in common at their lowest powers. For 12 = 2^2 x 3 and 18 = 2 x 3^2, the GCF is 2 x 3 = 6. The Euclidean algorithm is fastest for large numbers.
What is the GCF used for?
The greatest common factor is mainly used to simplify fractions — divide numerator and denominator by their GCF to reduce to lowest terms. It also helps factor algebraic expressions, split quantities into equal groups, and solve word problems about distributing items evenly without leftovers.
What is the Euclidean algorithm?
It is a fast way to find the GCF of two numbers: replace the larger number with the remainder of dividing the larger by the smaller, and repeat until the remainder is zero. The last non-zero remainder is the GCF. For 48 and 60: 60 mod 48 = 12, 48 mod 12 = 0, so the GCF is 12.
What does it mean if the GCF is 1?
If the greatest common factor of two numbers is 1, they share no common factors other than 1 and are called coprime or relatively prime. For example, 8 and 9 are coprime even though neither is itself prime. Coprime numerator and denominator means a fraction is already in lowest terms.
What is the difference between GCF and LCM?
The GCF (greatest common factor) is the largest number that divides all the inputs, while the LCM (least common multiple) is the smallest number all the inputs divide into. They are linked: for two numbers, GCF(a,b) x LCM(a,b) = a x b. GCF is used to simplify fractions; LCM is used to add them.
Is the 'lowest common divisor' the same as the GCF?
People searching 'lowest common divisor' almost always want the greatest common factor — the largest number dividing both (GCF of 24 and 36 is 12). Taken literally, the lowest common divisor of any two integers is just 1, which is never useful. The other companion concept is the LCM, the smallest shared multiple (72 for 24 and 36); GCF × LCM = the product of the two numbers.