What is true about the greatest common factor of a set of numbers?

The correct understanding of the greatest common factor (GCF) of a set of numbers is that it cannot be greater than the smallest number in that set. The GCF is defined as the largest number that divides all the numbers in the set without leaving a remainder. Since the GCF must be a factor of each individual number, it logically follows that it must be less than or equal to the smallest number in the set.

For instance, if you consider the set of numbers 8 and 12, the GCF is 4, which is less than the smallest number, 8. If the smallest number in a set is x, any factor that is common to all members of the set cannot exceed x; otherwise, it would not be a common factor for at least one of the other numbers. Thus, the GCF must always be less than or equal to the smallest number present, supporting the notion stated.