GCF Calculator
Find the greatest common factor (GCF, also called GCD or HCF) of two or more whole numbers.
Greatest common factor
12
- Each number ÷ GCF
- 4, 15, 50
Show the work
Euclid's algorithm
gcd(a, b) = gcd(b, a mod b)
gcd(48, 180) = gcd(180, 48) = gcd(48, 36) = gcd(36, 12) = gcd(12, 0) = 12
Then the next number
gcd(a, b) = gcd(b, a mod b)
gcd(12, 600) = gcd(600, 12) = gcd(12, 0) = 12
How it works
Euclid's algorithm: gcd(a, b) = gcd(b, a mod b) until the remainder is 0; gcd of a list folds pairwise
Questions
- How does the GCF calculator work?
- Euclid's algorithm: gcd(a, b) = gcd(b, a mod b) until the remainder is 0; gcd of a list folds pairwise.
- What do I need to enter?
- Whole numbers. Optional fields can be left blank.
Related tools
- LCM CalculatorFind the least common multiple (LCM) of two or more whole numbers — exact, however large.
- Modulo CalculatorFind a mod n — the remainder after division — with both the math (always positive) and programming conventions.
- Quadratic Equation SolverSolve ax² + bx + c = 0 for real or complex roots, with the discriminant and vertex.
- Cubic Equation SolverSolve ax³ + bx² + cx + d = 0 for all three roots, real or complex.
- FOIL CalculatorMultiply two binomials (ax + b)(cx + d) with the FOIL method and see each step.
- Completing the Square CalculatorRewrite ax² + bx + c in vertex form a(x − h)² + k by completing the square.
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