What is the GCF used for?

GCF is commonly used to simplify fractions to their lowest terms — dividing both the numerator and denominator by their GCF.

What if the numbers share no common factor besides 1?

Then their GCF is 1, and they're called 'coprime' — this is a valid and common result, not an error.

GCF Calculator

Find the greatest common factor (GCF), also called the greatest common divisor, of two or more numbers.

Numbers (comma or space separated)

Greatest Common Factor

How It Works

The Euclidean algorithm

The GCF is found using the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller number, until the remainder is 0 — the last non-zero value is the GCF.

Example Calculation

The GCF of 12 and 18 is 6 — the largest number that divides evenly into both.

Common Mistakes

Confusing GCF with LCM — GCF is the largest shared factor (smaller than or equal to the smallest input), while LCM is the smallest shared multiple (bigger than or equal to the largest input).
Listing out all factors by hand for large numbers instead of using the much faster Euclidean algorithm.

Frequently Asked Questions

What is the GCF used for?: GCF is commonly used to simplify fractions to their lowest terms — dividing both the numerator and denominator by their GCF.
What if the numbers share no common factor besides 1?: Then their GCF is 1, and they're called 'coprime' — this is a valid and common result, not an error.