Find the GCF of two or more numbers using the Euclidean algorithm
This GCF (Greatest Common Factor) calculator, also known as the GCD (Greatest Common Divisor) calculator, finds the largest positive integer that divides all given numbers. It uses the efficient Euclidean algorithm and also displays the LCM for reference.
The algorithm repeatedly replaces the larger number by the remainder of dividing the larger by the smaller, until one becomes zero. The remaining non-zero number is the GCD. This method is much faster than enumerating factors for large numbers.
GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are the same concept. Both refer to the largest positive integer that divides evenly into all given numbers. "GCF" is more common in algebra, while "GCD" is more common in number theory.
GCF is used when simplifying fractions, dividing items into equal groups, determining the largest tile size for tiling a floor, and solving problems involving ratios or proportions. For example, to simplify 36/48, divide both by their GCF of 12 to get 3/4.