Find the Greatest Common Factor (GCF) — also called HCF or GCD — of two or more numbers with prime factorization.
This tool calculates the Greatest Common Factor (GCF), also called the Greatest Common Divisor (GCD), of two or more numbers — the largest number that divides evenly into all of them. GCF is used in simplifying fractions, factoring algebraic expressions, and solving problems involving equal grouping.
The calculator commonly uses the Euclidean algorithm, which repeatedly applies the rule GCF(a, b) = GCF(b, a mod b) until the remainder reaches zero, at which point the last non-zero value is the GCF. It can also be found by listing all factors of each number and identifying the largest one they share.
Enter two or more numbers, and the calculator returns their greatest common factor.
Example: The GCF of 24 and 36 is 12, since 12 is the largest number that divides evenly into both 24 (24 ÷ 12 = 2) and 36 (36 ÷ 12 = 3).
Why is GCF useful for simplifying fractions? Dividing both the numerator and denominator of a fraction by their GCF reduces it to its simplest form — for example, 24/36 simplifies to 2/3 by dividing both by their GCF of 12.
What's the difference between GCF and LCM? GCF (Greatest Common Factor) is the largest number that divides evenly into a set of numbers, while LCM (Least Common Multiple) is the smallest number that all the given numbers divide evenly into — they solve opposite types of problems.
What is the Euclidean algorithm? It's an efficient method for finding the GCF of two numbers by repeatedly replacing the larger number with the remainder of dividing it by the smaller number, until the remainder is zero.
Can GCF be calculated for more than two numbers? Yes, GCF can be found for any set of numbers by finding the GCF of the first two, then finding the GCF of that result with the next number, and so on.
What is the GCF of two prime numbers? If the two prime numbers are different, their GCF is always 1, since prime numbers by definition have no common factors other than 1.