How is the greatest common factor (GCF) of two numbers determined?

The greatest common factor (GCF) of two numbers is determined by finding the highest number that divides both of the numbers without leaving a remainder. This means that when you divide each of the two numbers by the GCF, the result will be an integer for both, indicating that it is a common factor.

To find the GCF, one typically lists out the factors of each number and identifies the largest one that appears in both lists, or employs methods such as prime factorization or the Euclidean algorithm. This process allows for a clear understanding of the relationship between the two numbers in terms of divisibility.

The other options do not accurately describe the GCF: the smallest number that divides both would not capture the essence of being the greatest; the sum of the numbers and their product are unrelated to common factors.