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. There are various methods to calculate the GCD, including the Euclidean algorithm, which involves repeated division. Understanding the GCD helps in various mathematical applications, including reducing ratios and optimizing calculations.