GCF/GCD Calculator
Calculate the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD) of two or more numbers. Uses the Euclidean algorithm with step-by-step explanation.
Inputs
Results
Greatest Common Factor (GCF)
12
Least Common Multiple (LCM)144
All Common Divisors1, 2, 3, 4, 6, 12
Number of Common Divisors6
Are Numbers Coprime?No
Euclidean Algorithm StepsUsing Euclidean Algorithm for GCD(48, 36):
48 = 36 × 1 + 12
36 = 12 × 3 + 0
GCD = 12
How to Use This Calculator
- Enter two required numbers and up to two optional additional numbers in the Number fields.
- The Greatest Common Factor (GCF/GCD) is the largest integer that divides all entered numbers evenly, computed via the Euclidean algorithm.
- Are Coprime? indicates whether the GCF equals 1 — coprime numbers share no common factors other than 1.
- The Least Common Multiple is also computed: LCM = (n1 × n2) / GCF — useful for adding fractions with different denominators.
- All Common Divisors lists every shared factor, giving insight into divisibility relationships.
- Use positive integers only; the algorithm is undefined for zero or negative inputs.
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Formula
GCD(a, b) = GCD(b, a mod b)Related Calculators
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