What is defined as the largest common factor of two or more given numbers?

The largest common factor of two or more given numbers is referred to as the greatest common factor (GCF). This term describes the highest number that can evenly divide each of the given numbers without leaving a remainder.

For example, if we are determining the GCF of the numbers 12 and 18, we identify the factors of each number: 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 are 1, 2, 3, and 6, making 6 the largest of these, which is why the greatest common factor of 12 and 18 is 6.

In contrast, the least common multiple (LCM) represents the smallest number that is a multiple of both (not the largest factor), while sum refers to the total obtained by adding numbers, and product involves multiplying numbers together. Understanding these definitions clarifies why the term greatest common factor correctly answers the question about identifying the largest common factor.