🔢 GCF Calculator
Find the greatest common factor of numbers
Enter two or more positive integers separated by commas
How GCF Calculation Works
Formula
GCF via Euclidean Algorithm: GCF(a, b) = GCF(b, a mod b)
- 1Enter two or more numbers.
- 2The calculator finds the prime factorization of each number.
- 3Common prime factors are identified.
- 4The GCF is the product of the lowest powers of common primes.
- 5Alternatively, the Euclidean algorithm is applied for efficiency.
About GCF Calculator
Calculate the Greatest Common Factor (GCF) of two or more numbers. Also known as GCD (Greatest Common Divisor). Shows step-by-step prime factorization and Euclidean algorithm.
Frequently Asked Questions
What is the GCF used for?
GCF is used to simplify fractions (divide numerator and denominator by GCF), find common denominators, solve problems in number theory, and in practical applications like cutting materials into equal pieces.
What is the difference between GCF and LCM?
GCF is the largest number that divides all given numbers evenly. LCM is the smallest number that all given numbers divide into evenly. They are related: GCF × LCM = Product of the two numbers.
Can the GCF be 1?
Yes. When the GCF of two numbers is 1, they are called 'coprime' or 'relatively prime'. For example, GCF(8, 15) = 1 because they share no common factors other than 1.