GCF Calculator
Find the Greatest Common Factor (GCF) — also called GCD — of two or more integers. Uses prime factorization with full working shown. Essential for simplifying fractions, factoring expressions, and solving word problems.
Enter two or more integers separated by commas (e.g., 24, 36, 48). The calculator finds the GCF using prime factorization, lists all common factors, and shows the step-by-step working.
Algorithm used: Euclidean Algorithm (also shows prime factorization breakdown for verification).
Example: GCF(24, 36) = 12, because 12 is the largest number that divides both 24 and 36 evenly.
GCF (or GCD) is found by: 1. Prime factorization method: factor each number and multiply the common prime factors raised to their lowest powers. GCF(24, 36): 24 = 2³ × 3, 36 = 2² × 3² → GCF = 2² × 3 = 12
2. Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), recursing until remainder = 0. GCF(24, 36): GCF(36, 24) → GCF(24, 12) → GCF(12, 0) = 12
For multiple numbers: GCF(a, b, c) = GCF(GCF(a, b), c).
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