Greatest Common Factor (GCF) Calculator
Find the GCF / HCF of two or more numbers.
Greatest Common Factor (GCF) Calculator
Find the greatest common factor (GCF / HCF) of two or more numbers using prime factorization or Euclidean algorithm.
What is the Greatest Common Factor (GCF) Calculator and How Does It Work?
The GCF Calculator (also called HCF, Highest Common Factor) finds the largest number that divides two or more numbers evenly with no remainder, using the efficient Euclidean algorithm.
The Euclidean algorithm repeatedly replaces the larger number with the remainder of dividing it by the smaller number, until the remainder reaches zero - the last non-zero remainder is the GCF.
24 = 2³×3, 36 = 2²×3²; the shared factors give GCF = 2²×3 = 12.
The GCF is found pairwise: GCF(12,18)=6, then GCF(6,30)=6.
Common Real-World Use Cases
Divide a numerator and denominator by their GCF to reduce a fraction to its simplest form.
Find the largest group size that divides several different item counts evenly.
Factor out the greatest common factor from algebraic expressions before further simplification.
- 1Enter two or more numbers separated by commas or spaces.
- 2The calculator applies the Euclidean algorithm pairwise across all numbers.
- 3View the greatest common factor along with the calculation steps.
- •The GCF of any number and 0 is the number itself.
- •If two numbers share no common factor besides 1, they are called "coprime" and their GCF is 1.
Frequently Asked Questions
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