GCF Calculator

Find the Greatest Common Factor (GCF) of up to 10 numbers using the Euclidean algorithm.

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e.g. 12, 18, 24

GCF (GCD)

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LCM

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Find the Greatest Common Factor (GCF, also called GCD) of up to 10 numbers using the Euclidean algorithm, with full working shown.

How It Works

How GCF Calculator Works

The Greatest Common Factor is the largest number that divides evenly into every number in your list. The calculator finds it using the Euclidean algorithm, an efficient method that repeatedly replaces the larger of two numbers with the remainder of dividing it by the smaller, until the remainder reaches zero — the last non-zero remainder is the GCF.

For more than two numbers, the calculator applies the Euclidean algorithm to the first pair, then combines that result with each remaining number in turn, since GCF(a, b, c) = GCF(GCF(a, b), c).

The results also show the LCM of the same numbers, each number divided by the GCF (revealing the smallest equivalent ratio between them), and a full list of factors for each individual number, so you can cross-check the answer by inspection as well as by algorithm.

Worked Example

See It In Action

For 12, 18, and 24, the Euclidean algorithm on 12 and 18 gives: 18 = 1×12 + 6, then 12 = 2×6 + 0, so GCF(12, 18) = 6. Combining with 24: 24 = 4×6 + 0, so the GCF stays 6. Dividing each number by 6 gives the ratio 2 : 3 : 4 — the simplest form of the relationship between them.

Real-World Use Cases

Who Uses GCF Calculator and Why

Reducing a fraction to lowest terms by dividing both numerator and denominator by their GCF.
Splitting a quantity — like a batch of supplies or a group of people — into the largest possible number of equal groups with nothing left over.
Finding the largest square tile size that evenly fills a rectangular floor with given width and length.
Simplifying a ratio between three or more quantities down to its smallest whole-number form.

Common Mistakes

Mistakes to Avoid

Confusing GCF with LCM — GCF shrinks toward your numbers (it's never larger than the smallest one), while LCM grows past them; mixing the two up gives a completely wrong-scale answer.
Trying to list every factor of large numbers by hand to find the GCF instead of trusting the Euclidean algorithm, which gets the same answer in only a few division steps regardless of size.
Assuming a GCF of 1 means something went wrong — it just means the numbers are coprime and share no factor larger than 1, which is a valid and common result.

Pro Tips

Tips for Best Results

Use the "divided by GCF" ratio shown in the results directly when you need to simplify a proportion or scale a recipe, rather than recalculating it separately.
For more than two numbers, remember the calculator combines them pairwise (GCF of the first two, then with the next, and so on) — the order you enter them in doesn't change the final answer.

Troubleshooting

Fixing Common Problems

The GCF came back as 1 and I expected a bigger shared factor. — A GCF of 1 means the numbers are genuinely coprime — double-check your inputs are the numbers you intended, since it's a valid result, not an error.

I need the GCF of more than 10 numbers. — Combine them in batches: find the GCF of the first group, then combine that result with each remaining number using GCF(a, b, c) = GCF(GCF(a, b), c).

Glossary

Terms Explained

Greatest Common Factor (GCF): The largest number that divides evenly into every number in a set — also called the GCD.

Euclidean algorithm: A method for finding the GCF by repeatedly replacing the larger of two numbers with the remainder of dividing it by the smaller, until the remainder reaches zero.

FAQ

Frequently Asked Questions

What is the difference between GCF and GCD?

Nothing mathematically — "Greatest Common Factor" and "Greatest Common Divisor" are two names for the exact same value, the largest number that divides evenly into all the numbers in a set. GCF is more common in school textbooks; GCD is more common in computer science.

Why use the Euclidean algorithm instead of listing all factors?

Listing every factor works fine for small numbers, but becomes slow for large ones. The Euclidean algorithm finds the GCF in only a handful of division steps regardless of how large the numbers are, which is why it is the standard method used in practice.

What does it mean if the GCF of my numbers is 1?

A GCF of 1 means the numbers are "coprime" or "relatively prime" — they share no common factors other than 1, even if none of them are individually prime numbers.

How is GCF used with fractions?

Dividing both the numerator and denominator of a fraction by their GCF reduces it to lowest terms — for example, 18/24 simplifies to 3/4 by dividing both by their GCF of 6.