greatest common divisor

The greatest common divisor (GCD) of two numbers is the largest number that divides both of them exactly, without leaving a remainder. For example, for 8 and 12, the GCD is 4, because 4 divides both 8 and 12 evenly, and no larger number does. It helps identify common factors between numbers and is useful for simplifying fractions, solving problems involving divisibility, and finding common measures. The GCD is unique and can be found using methods like prime factorization or the Euclidean algorithm.