How can you find the GCF of two numbers?

To find the greatest common factor (GCF) of two numbers, the best approach is to list the factors of each number and identify the largest one that they share. This method allows you to systematically see which numbers divide evenly into both numbers and thereby pinpoint the largest factor common to both.

For instance, if you are looking to find the GCF of 12 and 18, you would list the factors of each: 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. Comparing these lists, the common factors are 1, 2, 3, and 6, with 6 being the greatest. Thus, the GCF of 12 and 18 is 6.

This method is effective because it works for any two positive integers and provides a clear visual of their shared factors. Other methods, such as adding or multiplying the numbers, do not address the specific need to find commonality in factors, nor do they yield the GCF. Identifying the largest number doesn't necessarily lead to the GCF, as the largest