How do you find the greatest common factor (GCF) of two numbers?

Finding the greatest common factor (GCF) involves identifying the largest positive integer that can divide both numbers without leaving any remainder. When determining the GCF, one is essentially looking for the highest number that both values share as a factor. This means that if you divide both numbers by this integer, the result will be whole numbers, confirming that there is no remainder.

For example, if you want to find the GCF of 12 and 18, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors here are 1, 2, 3, and 6, and among those, 6 is the largest. Therefore, the GCF of 12 and 18 is 6.

This method ensures that the GCF is not only a factor of both numbers but also the largest such factor, which is key to solving problems involving divisibility and simplification of fractions.