GCF Calculator

Find the Greatest Common Factor (GCF / GCD) and Least Common Multiple (LCM) with complete step-by-step methods.

Greatest Common Factor (GCF) Solver

Enter positive integers separated by commas or spaces (e.g., 18, 24, 36 or 12 20).

Numbers:

The GCF (also known as Greatest Common Divisor / GCD) is the largest positive integer that divides two or more integers without leaving a remainder.

1. Euclidean Algorithm: GCF(a, b) = GCF(b, a mod b)

2. Prime Factorization: GCF = Product of common prime factors with lowest powers

3. Listing Factors: Find all factors for each number and select the highest common one

There is no difference! GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) refer to the exact same mathematical value.

If the GCF of two or more numbers is 1, those numbers are called coprime or relatively prime (for example, 8 and 15).

Yes. The calculator supports finding the greatest common factor of multiple integers entered together.

The calculator may use efficient mathematical methods such as the Euclidean Algorithm and prime factorization to determine the GCF.

GCF is commonly used for simplifying fractions, algebra, factorization, engineering calculations, and solving mathematical problems.