GCF Calculator
Find the greatest common factor of two or more positive whole numbers. GCF, GCD and HCF are names for the same value: the largest integer that divides every number in the list with no remainder.
GCF Calculator tool
About the GCF Calculator
The calculator uses the Euclidean algorithm pairwise. Remainders replace the larger number until a remainder is 0; the last nonzero remainder is the GCF. It does not return 0 as a classroom factor — inputs must be at least 1.
Reducing a fraction a/b is divide both parts by GCF(a, b). This page reports the GCF. The fraction calculator applies that reduction after an operation. The LCM calculator is the counterpart for common multiples.
How the GCF Calculator works
Euclid: GCF(a, b) = GCF(b, a mod b), and GCF(a, 0) = |a|. For more than two numbers, GCF(a, b, c) = GCF(GCF(a, b), c).
Worked: GCF(48, 18) → 48 = 2×18 + 12, 18 = 1×12 + 6, 12 = 2×6 + 0, so GCF = 6. Then GCF(6, 30) = 6.
GCF(a, b) = GCF(b, a mod b)
GCF(a, 0) = |a|
GCF(a, b, c) = GCF(GCF(a, b), c)
Example
GCF(48, 18, 30) = 6, the default on this page.
How to Use the GCF Calculator
- Enter 2 to 12 positive whole numbers.
- Read the greatest common factor.
- If the GCF is 1, the numbers are coprime — they share no prime factor.
- To reduce a fraction, divide numerator and denominator by this GCF.
- Use the factor calculator if you want every divisor of a single number.
GCF Calculator Examples
Two numbers
GCF(54, 24) = 6. 54 = 2 × 3³, 24 = 2³ × 3, shared primes 2¹ × 3¹ = 6.
Three numbers
GCF(48, 18, 30) = 6. Each is divisible by 6; 12 does not divide 18 or 30.
Coprime pair
GCF(17, 19) = 1. Consecutive integers are always coprime.
Powers
GCF(16, 24) = 8. Keep the lowest power of each shared prime: 2⁴ and 2³×3 share 2³.
How to Find GCF by Prime Factors
Factor each number, then multiply the primes that appear in every factorization, using the smallest exponent. 48 = 2⁴ × 3, 18 = 2 × 3², 30 = 2 × 3 × 5. Shared: 2¹ × 3¹ = 6. Listing all factors and picking the overlap works for small numbers and is slower for 12-digit inputs — Euclid only needs remainders, which is why the tool uses it.
Using GCF to Simplify a Fraction
54/24 divided by GCF 6 is 9/4. The ratio 54:24 simplifies to 9:4 the same way. The fraction calculator will also reduce after you add or multiply. This GCF calculator is the shared-divisor step when you already have the two integers.
GCF versus LCM
For two numbers, product = GCF × LCM. That check is a good homework audit: 54 × 24 = 1,296 and 6 × 216 = 1,296. It does not hold in the same simple form for three numbers. If you needed a common multiple (when to line up repeating events, or a common denominator), switch to the LCM calculator.
| Numbers | GCF | Coprime? |
|---|---|---|
| 54, 24 | 6 | No |
| 48, 18, 30 | 6 | No |
| 17, 19 | 1 | Yes |
| 16, 24 | 8 | No |
| 100, 45, 80 | 5 | No |
| 9, 28 | 1 | Yes |
Word problems GCF actually solves
Splitting 48, 18 and 30 items into identical bundles with none left over uses GCF 6 — six bundles of 8, 3 and 5. Tiling a 48-by-18 rectangle with the largest square tiles also uses GCF (here 6). Those are packing problems, not percentages. Use the percentage calculator only if the question is “what percent is 18 of 48.”
Frequently Asked Questions
Are GCF, GCD and HCF different?
No. Greatest common factor, greatest common divisor and highest common factor are the same integer. This page uses GCF in the result label.
What does a GCF of 1 mean?
The numbers are coprime. They still have 1 as a trivial common factor.
Can I simplify a ratio here?
The GCF is the number you would divide by. The ratio calculator applies that division and prints A:B in lowest terms.
Why not allow 0?
GCF(0, n) = n mathematically. This form is built for positive counting numbers used in homework lists.
How many numbers can I paste?
2 to 12, each from 1 through 1,000,000,000,000.
Is this prime factorization?
No. It only reports the shared factor. Open the factor calculator for the full list of divisors of one integer.
Guides that use this calculator
- How to Simplify a Ratio (and Find Equivalents)
A ratio is part-to-part. Divide by the GCF to simplify, or scale both terms for an equivalent. The free ratio calculator does both.
- How to Find Factors of a Number
Factors come in pairs up to the square root. Here is the list for 84, prime factorization, and the free factor calculator — not factorial n!.
- How to Find GCF (Greatest Common Factor)
GCF is the largest integer that divides every input. Euclid’s algorithm, a 48-18-30 example and the free GCF calculator.