The greatest common factor (GCF) is the largest number that can evenly divide two or more numbers without leaving a remainder. For example, if you have the numbers 12 and 18, the factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, 6, and the GCF is 6. Finding the GCF is useful in simplifying fractions, solving problems in algebra, and determining common denominators. To calculate the GCF, you can list the factors of each number or use methods like prime factorization or the Euclidean algorithm. Understanding the GCF helps in various mathematical applications.