✂️ GCF Calculator
The greatest common factor is the largest integer dividing both numbers — it is how you reduce fractions and simplify ratios. Euclid's algorithm finds it fast by repeated division, no factor lists needed.
Enter two integers. You get the GCF and a coprime verdict: numbers sharing no factor but 1 are coprime, like 7 and 13.
How to use this calculator
Type two integers and press Calculate to get their greatest common factor.
- Type the first integer into the First integer field.
- Type the second integer into the Second integer field.
- Press Calculate and read the GCF as the headline result.
- Check the coprime line: Yes means the numbers share no factor besides 1.
Frequently asked questions
What is the greatest common factor?
The largest integer that divides both numbers evenly. The GCF of 12 and 18 is 6, the biggest number on both factor lists. It is also called the greatest common divisor (GCD).
How is the GCF calculated?
With Euclid's algorithm: repeatedly replace the larger number by the remainder of dividing it by the smaller one, until the remainder is zero. The last non-zero remainder is the GCF.
What does coprime mean?
Two numbers are coprime when their GCF is 1, meaning they share no factors. 7 and 13 are coprime; 12 and 18 are not.
Where is the GCF used?
Reducing fractions to lowest terms, simplifying ratios, and splitting things into the largest equal groups with nothing left over.