About this GCF calculator
The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor (HCF), is the largest whole number that divides every number in a set without a remainder. It is used to simplify fractions, split things into equal groups, and solve number problems. This calculator shows three ways to find it. The Euclidean algorithm repeatedly replaces the larger number with the remainder of a division until the remainder is 0. Prime factorization multiplies the prime factors the numbers share. Listing factors writes out every divisor and picks the largest one they have in common.
How to find the greatest common factor
- Enter your numbers. Type 2 to 15 positive whole numbers separated by commas or spaces, or press an example.
- Choose a method. Show all three methods, or only the one your class uses: the Euclidean algorithm, prime factorization, or listing factors.
- Press Find GCF. Read the GCF and follow the steps. Common factors are highlighted in the factor lists.
Frequently asked questions
What is the GCF of 24 and 36?
It is 12. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, and those of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest number in both lists is 12.
How does the Euclidean algorithm work?
Divide the larger number by the smaller one and keep the remainder. Repeat with the smaller number and the remainder until the remainder is 0; the last divisor is the GCF. For 36 and 24: 36 = 24 × 1 + 12, then 24 = 12 × 2 + 0, so the GCF is 12.
How do I find the GCF of three or more numbers?
Find the GCF of the first two, then the GCF of that result and the next number, and so on. The calculator does this for up to 15 numbers and shows each pair.
What does coprime mean?
Numbers are coprime, or relatively prime, when their GCF is 1. They need not be prime themselves: 8 and 15 are coprime even though neither is a prime number.
Are GCF, GCD, and HCF the same thing?
Yes. Greatest common factor, greatest common divisor, and highest common factor are different names for the same number, used in different countries and textbooks.