The greatest common divisor (GCD) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, since 6 is the highest number that can evenly divide both 12 and 18. Finding the GCD is useful in simplifying fractions and solving problems in number theory. To calculate the GCD, various methods can be used, including listing the divisors, using the prime factorization of the numbers, or applying the Euclidean algorithm. The GCD helps in understanding the relationships between numbers and is a fundamental concept in mathematics.