GCF Calculator
Find the greatest common factor (GCF) of two or more numbers instantly. This free GCF calculator shows the step-by-step Euclidean algorithm working, and includes the least common multiple (LCM) as a bonus result.
How to Use This Calculator
- Enter two or more whole numbers, separated by commas or spaces (e.g. 48, 18, 30).
- Click Calculate.
- See the GCF highlighted at the top, with the full step-by-step Euclidean algorithm working below.
- Check the bonus LCM result at the bottom.
What is the Greatest Common Factor?
The greatest common factor (GCF) — also called the greatest common divisor (GCD) — of two or more numbers is the largest whole number that divides each of them exactly, with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest factor they share is 6, so GCF(12, 18) = 6.
The fastest way to find the GCF by hand is the Euclidean algorithm: divide the larger number by the smaller one, take the remainder, then repeat using the divisor and the remainder until a remainder of zero appears. The last non-zero remainder is the GCF. This calculator performs exactly those steps for you and shows every one of them, so you can follow along and learn the method.
The GCF is used to simplify fractions (divide the numerator and denominator by their GCF), to split items into the largest possible equal groups, and in scheduling problems where repeating cycles must line up. It is closely related to the least common multiple (LCM): for any two numbers, GCF × LCM equals their product. That is why this free GCF calculator displays both values together.
The GCF of a set of numbers is the largest integer d that divides every number in the set exactly.
Example: GCF(48, 18) = 6 because 6 is the largest number that divides both 48 and 18.
Worked Examples
Example 1: GCF(48, 18). 48 = 18 × 2 + 12; 18 = 12 × 1 + 6; 12 = 6 × 2 + 0. The last non-zero remainder is 6, so GCF = 6 and LCM = 144.
Example 2: GCF(12, 18, 24). First GCF(12, 18) = 6, then GCF(6, 24) = 6, so GCF = 6 and LCM = 72.
Example 3: GCF(7, 13) = 1. The numbers share no factor besides 1, so they are called coprime.
Our Testing Process
Every DaProfitClub tool is tested before publishing. We verify GCF results against known factor pairs and reference calculators, test edge cases (zeros, large numbers, and more than two inputs), and confirm the tool works on desktop and mobile browsers.
Frequently Asked Questions
What is the difference between GCF and LCM?
The GCF is the largest number that divides all of your numbers, while the LCM is the smallest number that all of your numbers divide into. For any two numbers, GCF × LCM equals their product. This calculator shows both values.
Can I find the GCF of more than two numbers?
Yes. Enter as many whole numbers as you like, separated by commas or spaces. The calculator applies the Euclidean algorithm pair by pair — for example, GCF(12, 18, 24) is computed as GCF(GCF(12, 18), 24).
What is the GCF if one of the numbers is 0?
GCF(0, n) = n, because every number divides 0 exactly. The calculator handles zero inputs correctly.
What does it mean if the GCF is 1?
It means the numbers are coprime — they share no common factor besides 1. For example, GCF(7, 13) = 1.
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Last updated: September 30, 2026