🔢 Greatest Common Factor Calculator
Professional GCF calculator for finding the greatest common factor of two or more numbers. Uses Euclidean algorithm and prime factorization with step-by-step solutions.
GCF of Two Numbers
Calculate the greatest common factor of two numbers using the Euclidean algorithm.
GCF of Three Numbers
Calculate the greatest common factor of three numbers using iterative application of the Euclidean algorithm.
GCF of Multiple Numbers
Calculate the greatest common factor of multiple numbers. Enter numbers separated by commas.
About Greatest Common Factor Calculator
This calculator finds the greatest common factor (GCF) of two or more numbers using multiple methods:
Methods Used
- Euclidean Algorithm: Efficient method using division and remainders
- Prime Factorization: Breaking numbers into prime factors to find common ones
- Iterative Approach: For multiple numbers, applying GCF sequentially
Properties of GCF
- Commutative: GCF(a, b) = GCF(b, a)
- Associative: GCF(a, GCF(b, c)) = GCF(GCF(a, b), c)
- Distributive: GCF(ka, kb) = k × GCF(a, b) for any integer k
- Range: GCF is always a positive integer or zero
Applications
- Fractions: Simplifying fractions to lowest terms
- Number Theory: Solving Diophantine equations
- Cryptography: RSA algorithm and modular arithmetic
- Engineering: Gear ratios and mechanical systems
- Computer Science: Algorithm optimization and data structures
Examples
- GCF(12, 18): 6 (factors: 12=2×2×3, 18=2×3×3, common: 2×3=6)
- GCF(24, 36, 48): 12 (largest number dividing all three)
- GCF(7, 13): 1 (coprime numbers)
Note
This calculator provides accurate GCF calculations with detailed step-by-step solutions. For very large numbers, the Euclidean algorithm is more efficient than prime factorization.