What is the largest number that divides both 48 and 18? You could list every divisor of each and compare, or you could use a method that is more than 2,000 years old and needs only a handful of steps. Euclid's algorithm has a picture behind it: cut the largest possible squares off a rectangle until nothing is left over, and the side of the last square is the answer. Try it on your own numbers, first by subtracting, then with the much faster remainder version.
This article and its interactive demo were created with the help of generative AI and editorially reviewed.