Math & Statistics

What Is the Greatest Common Factor (GCF)?

The greatest common factor (GCF) of two or more whole numbers is the largest number that divides all of them without a remainder. It is also called the greatest common divisor (GCD) or highest common factor (HCF). The GCF of 12 and 18 is 6.

How to Find the GCF

One method lists the prime factors of each number and multiplies the primes they share, using the lowest power of each. Another is Euclid's algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero.

Where It Is Used

The GCF is used to simplify fractions: dividing 18/24 by their GCF of 6 gives 3/4.

🧮 Calculate It Yourself

Put Greatest Common Factor (GCF) into practice with these free calculators — no sign-up, nothing stored.

🔢 GCF & LCM Calculator Greatest common factor and least common multiple, with prime factorizations. Calculate → ➗ Fraction Calculator Add, subtract, multiply, and divide fractions and mixed numbers, with steps. Calculate →

🔗 Related Terms

Least Common Multiple (LCM) Mean (Average)

More Math & Statistics Terms

📖 Browse all glossary terms or explore all free calculators.

Last updated: September 27, 2026. This definition is for general educational purposes only. It is not financial, investment, tax, legal, or medical advice, and it does not recommend any product or course of action. For decisions about your own situation, consult a qualified professional.