How to Find GCF (Greatest Common Factor)
Published 2026-11-03
GCF calculator, gcd calculator and hcf calculator are the same search: the greatest common factor of two or more whole numbers. US worksheets say GCF; many others say GCD or HCF. The integer does not change.
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Run these formulas with your own numbers. Math stays in your browser.
Open GCF Calculator →Our GCF calculator runs the Euclidean algorithm on 2 to 12 positive integers. It does not list every factor of one number (that is the factor calculator) and it does not print a reduced fraction until you take the GCF to the fraction or ratio tool.
Open the GCF calculator
Paste the list. The default 48, 18, 30 should show 6. If the result is 1, the numbers are coprime.
Euclid in one line
Replace the larger number with the remainder until the remainder is 0. The last nonzero remainder is the GCF. For more than two numbers, fold the result into the next value.
GCF(a, b) = GCF(b, a mod b)
GCF(a, b, c) = GCF(GCF(a, b), c)
Worked example: 48, 18, 30
48 = 2×18 + 12, 18 = 1×12 + 6, 12 = 2×6 + 0, so GCF(48, 18) = 6. Then GCF(6, 30) = 6. Prime-factor check: shared 2 × 3 = 6.
| Numbers | GCF | Coprime? |
|---|---|---|
| 54, 24 | 6 | No |
| 48, 18, 30 | 6 | No |
| 17, 19 | 1 | Yes |
| 16, 24 | 8 | No |
Simplifying fractions and ratios
Divide both parts of 54/24 or 54:24 by GCF 6 to get 9/4 or 9:4. That is the whole reason many people search “gcf calculator.” The ratio calculator does the division; this page reports the divisor.
- Find the GCF of the two parts.
- Divide both by that GCF.
- If you needed a common multiple instead, switch to the LCM calculator.
Bundles, tiles and the Euclidean steps
A worksheet that says “largest identical bundles with none left over” is GCF. 48 red, 18 blue and 30 green split into 6 bundles of 8, 3 and 5. Tiling a 48-by-18 rectangle with the largest square tiles also uses GCF 6. Euclid is faster than listing every factor: 48 = 2×18 + 12, 18 = 1×12 + 6, 12 = 2×6 + 0, so 6. Fold in 30 and you still have 6. Prime factors give the same 6: keep the lowest shared exponents. The GCF calculator runs Euclid and stops there — it will not print the 12 factors of 48; that is the factor calculator. Consecutive integers are always coprime (GCF 1), which is why 17 and 19 show 1 and why you cannot cancel anything in 17/19.
Use the free tool
Run these formulas with your own numbers. Math stays in your browser.
Open GCF Calculator →Frequently Asked Questions
Are GCF, GCD and HCF different?
No. Three names, one integer.
What does GCF 1 mean?
The numbers share no prime factor other than the trivial 1.
Can I factor one number here?
No. Use the factor calculator for all divisors of a single n.
Why is 0 refused?
This form is for positive counting numbers used in homework lists.
Does product = GCF × LCM?
For two numbers, yes. Not in the same simple form for three.
Related calculators
GCF Calculator
Greatest common factor (GCD/HCF) of two or more whole numbers.
LCM Calculator
Least common multiple of two or more whole numbers.
Fraction Calculator
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Ratio Calculator
Simplify a ratio or find an equivalent ratio from one known term.