Find the greatest common factor of any numbers. This free GCF calculator (also GCD or HCF) returns the largest shared factor, lists all common factors, and shows the LCM too.
Your numbers
Enter two or more whole numbers. The GCF (also called GCD or HCF) is the largest number that divides every value with no remainder.
Greatest common factor
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Enter some numbers
Numbers used
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LCM (least common multiple)
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Count
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Relatively prime?
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Common factors
The GCF helps simplify fractions (divide top and bottom by it) and split things into equal groups. It uses whole numbers; decimals are rounded.
Use this free GCF calculator to find the greatest common factor of two or more numbers. Enter your values to get the largest number that divides them all, plus the common factors and the LCM.
What this GCF calculator does
A GCF calculator finds the greatest common factor — also called the GCD or HCF — the largest whole number that divides every value in your list without a remainder. It also lists the common factors and shows the LCM.
How the GCF is calculated
Use the Euclidean algorithm on each pair:
GCD(a, b) = GCD(b, a mod b), repeated to zero
The GCF of 24 and 36 is 12; for 8, 12 and 16 it’s 4. The calculator chains the rule across all your numbers.
GCF examples
Numbers
GCF
12, 18
6
24, 36
12
8, 12, 16
4
7, 13
1 (coprime)
What is the GCF used for?
The GCF is the key to simplifying fractions — dividing the numerator and denominator by it gives lowest terms. It’s also used to split quantities into the largest equal groups. When the GCF is 1, the numbers are relatively prime (coprime).
How to use the GCF calculator
Enter two or more numbers, separated by commas, spaces or new lines.
Read the greatest common factor.
See the common factors and LCM alongside.
GCF FAQ
How do I find the GCF?
Find the largest number that divides all your values evenly. A quick method is the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b), repeated until zero. The GCF of 24 and 36 is 12.
What is the greatest common factor?
It's the biggest whole number that divides every number in your set without a remainder. For 8, 12 and 16, it's 4.
Are GCF, GCD and HCF the same?
Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) are different names for the same thing.
What does it mean if the GCF is 1?
The numbers are relatively prime (coprime) — they share no common factor other than 1, like 7 and 13.
What is the GCF used for?
Simplifying fractions (divide top and bottom by the GCF) and splitting quantities into the largest equal groups are the most common uses.
Is the GCF calculator free?
Yes, this GCF calculator is completely free, needs no sign-up, and gives instant results in your browser.
