A walkthrough, end to end.
- 1
Enter two or more integers separated by commas, spaces, or newlines.
- 2
The calculator returns the greatest common factor (GCF) using the Euclidean algorithm.
- 3
Bonus: shows whether all the numbers are coprime (GCF = 1).
Euclidean algorithm
gcd(a, b) = gcd(b, a mod b), terminating when b = 0. Generalized to lists by reducing pairwise. Discovered ~300 BCE; remains the standard fast algorithm.
What you can do with this.
Simplifying fractions
30/45: gcd(30, 45) = 15. Divide both by 15 → 2/3. The GCF is the divisor that simplifies a fraction to lowest terms in one step.
Tiling / packaging
Pack rectangular boxes with no waste: dimensions need GCF ≥ 1. Specifically, the largest square tile that perfectly tiles a 144×84 floor has side GCF(144, 84) = 12.
Algebra simplification
Factor common terms from polynomial coefficients. e.g., 12x³ + 18x² + 6x has GCF = 6x → 6x(2x² + 3x + 1).
Coprime check
Two numbers are coprime if GCF = 1 (no common factors > 1). 14 and 25 are coprime; 14 and 21 share factor 7. Useful in cryptography and number theory.
Equal grouping
30 students in a class, 18 desks. Largest group size dividing both equally = GCF(30, 18) = 6. Useful for educational logistics.
Simplifying ratios
12:18 → divide by GCF = 6 → 2:3. Same operation as fraction simplification, applied to ratios. The Ratio Calculator handles this directly.
Beat synchronization
Two metronomes at 60 and 90 BPM coincide every gcd(60, 90) = 30 seconds. The GCF reveals natural coincidence cycles.
GCF calculator 2026 — what's current
Foundational number theory. Spreadsheets and calculators handle reliably. AI tools too. Stand-alone calculator wins for speed and verification.
Frequently asked.
Same thing. GCF (Greatest Common Factor) is more common in US schools; GCD (Greatest Common Divisor) is more common in math/CS contexts. Identical concept and calculation.
gcd(0, n) = n for any n. gcd(0, 0) = 0 (sometimes left undefined). The calculator follows the convention gcd(0, n) = n.
Yes — uses absolute values. GCF is always positive.
No. Calculations run entirely in your browser.