GCF Calculator

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more integers without a remainder. For example, the GCF of 12 and 18 is 6. It's very useful for simplifying fractions to their simplest form and reducing ratios.

This calculator uses the Euclidean algorithm discovered by the ancient Greek mathematician Euclid. This method uses the remainder from division to quickly find the greatest common factor. It's very efficient as even large numbers can produce results in just a few steps.

The greatest common factor is needed when simplifying fractions to their simplest form. For example, to simplify 24/36, you find the GCF of the numerator and denominator (which is 12) and divide both by it to get 2/3. This is very useful when solving math problems or calculating ratios in everyday life.

This calculator can find the GCF of not just two, but multiple numbers at once. When there are three or more numbers, it calculates by first finding the GCF of two numbers, then finding the GCF of that result with the next number, and so on.

The greatest common factor is an important concept from elementary school math through high school mathematics. It's essential when students practice fraction calculations or learn about ratios and proportions. It's also used in real life, such as finding the smallest common unit of rhythm in music or calculating the required size when arranging tiles.

Rather than just showing the result, you can see each step of the Euclidean algorithm. This helps you understand the calculation principle and learn how to calculate by hand. It's a very useful feature for educational purposes.