GCF Calculator (Greatest Common Factor)
Find the greatest common factor of two or more whole numbers, with every common factor, prime factorizations and the numbers reduced by the GCF.
The greatest common factor (GCF) is the largest whole number that divides every number in a list with no remainder. You need it to simplify fractions and ratios, to split things into the largest possible equal groups, or to factor an expression in algebra. Enter two or more whole numbers to get the GCF, every common factor, and the prime factorizations that explain the answer.
How to use this tool
- Type two or more whole numbers separated by commas or spaces, without thousands separators.
- Read the GCF and the full list of common factors.
- Check the table for each number’s prime factorization and factor list.
- Use "Divided by the GCF" for the simplest ratio or fraction.
Formula
GCF = product of the primes shared by every number, each raised to its lowest power
Write each number as a product of primes. A prime only counts if it appears in every factorization, and you take the smallest exponent it has in any of them. If no prime is shared, the GCF is 1 and the numbers are called relatively prime.
Example
For 24, 36 and 60: 24 = 2³ × 3, 36 = 2² × 3² and 60 = 2² × 3 × 5. The primes in all three are 2 (lowest power 2²) and 3 (lowest power 3¹), so the GCF is 2² × 3 = 12. Dividing each number by 12 gives the ratio 2 : 3 : 5, and the common factors are 1, 2, 3, 4, 6 and 12.
Frequently asked questions
Is the GCF the same as the GCD or HCF?
Yes. Greatest common factor, greatest common divisor and highest common factor are three names for the same number; which one you see depends on the country and the textbook.
How do I use the GCF to simplify a fraction?
Divide the top and bottom by their GCF. For 36/60 the GCF is 12, so 36/60 = 3/5, which cannot be reduced any further.
What is the GCF of a number and 0?
Every whole number divides 0, so the GCF of 0 and n is n itself. The GCF of 0 and 0 is undefined, because there is no largest divisor.
What does a real GCF problem look like?
Cutting ribbons of 24 cm, 36 cm and 60 cm into equal pieces with no waste: the longest possible piece is the GCF, 12 cm, which gives 2 + 3 + 5 = 10 pieces.
Last updated: 2026-10-30