What do we call the process of finding the greatest common factor of two numbers?

The process of finding the greatest common factor of two numbers is commonly referred to as the GCD, or Greatest Common Divisor. This term directly describes the greatest integer that can divide both numbers without leaving a remainder. The concept is fundamental in number theory, as it helps in simplifying fractions, determining shared factors among numbers, and solving problems involving divisibility.

When calculating the GCD, various methods can be utilized, including listing out factors, using prime factorization, or applying the Euclidean algorithm, all of which essentially lead to identifying this greatest divisor.

In contrast, the least common multiple (LCM) refers to the smallest multiple that two numbers share, which is a different concept than finding the GCD. Factoring generally involves expressing a number as a product of its prime factors, and dividing is simply performing a mathematical operation. Thus, GCD is the specific term used for the process involving the greatest common factor of two numbers.