What is the greatest common factor?

The greatest common factor, often abbreviated as GCF, refers to the largest positive integer that divides each of the given numbers without leaving a remainder. This concept is crucial in simplifying fractions, finding common denominators, and solving problems involving divisibility.

Understanding that the GCF is the biggest factor shared by two or more numbers distinguishes it from concepts like the least common multiple (LCM). While other options touch on related mathematical principles, they focus on different aspects—such as identifying the smallest common or largest common multiples, which are distinct from the factors being considered.

In summary, the definition of the greatest common factor as the largest common factor aligns accurately with mathematical terminology and application, highlighting its importance in various arithmetic operations.