GCF (Greatest Common Factor): The largest positive integer that divides evenly into every number you entered. It's the biggest "shared building block" of your set.
Prime Factorization: Each number broken into its prime factors (2, 3, 5, 7, …). The GCF is the product of all prime factors that appear in every number's factorization.
GCF of 1: If the result is 1, the numbers are coprime — they share no prime factors other than 1.
How This Calculator Works
You enter two or more positive whole numbers separated by commas. The tool uses Euclid's algorithm to efficiently find the GCF by repeatedly dividing and taking remainders. It also shows the prime factorization of each number so you can visually confirm which factors are shared.
Quick Questions
Is the GCF the same as the GCD?
Yes. Greatest Common Factor (GCF), Greatest Common Divisor (GCD), and Highest Common Factor (HCF) all mean the same thing — the largest number that divides evenly into all given numbers.
How do I use the GCF to simplify a fraction?
Divide both the numerator and denominator by their GCF. For example, 12/18 has a GCF of 6, so it simplifies to 2/3.
What is Euclid's algorithm?
It's a method for finding the GCD of two numbers by repeatedly replacing the larger number with the remainder of dividing the larger by the smaller, until one number becomes zero. The other number is the GCD.
Can I find the GCF of more than two numbers?
Yes. Find the GCF of the first two numbers, then find the GCF of that result with the third number, and so on. This calculator handles any number of inputs automatically.