Greatest Common Factor Calculator
Calculate the Greatest Common Factor (GCF) of multiple numbers with detailed prime factorization steps and highlighted common factors.
Calculate the Greatest Common Factor (GCF) of multiple numbers with detailed prime factorization steps and highlighted common factors.
Enter Numbers
Enter positive integers separated by commas
About Greatest Common Factor
The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides all the given numbers without a remainder. It's found by identifying the common prime factors with their minimum powers.
Key Properties:
- • GCF(a, b) × LCM(a, b) = a × b
- • GCF is associative: GCF(a, GCF(b, c)) = GCF(GCF(a, b), c)
- • GCF of coprime numbers is 1
- • GCF of a number and 0 is the number itself
- • GCF divides all given numbers
Common Applications:
- • Simplifying fractions to lowest terms
- • Finding equivalent ratios
- • Cryptography and number theory
- • Computer science algorithms
- • Mathematical problem solving
Calculation Method:
GCF is calculated using prime factorization. For each prime factor that appears in all numbers, we take the minimum power. The product of these common factors gives us the GCF. Common factors are highlighted with underlines in the factorization.