Problem:
How many factors of have more than factors? (As an example, has factors, namely and .)?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let's begin by factoring :
These twelve factors of can be classified by the number of their factors: has one factor. each have two factors. has three distinct factors. Thus, all the remaining seven numbers must have more than three factors. Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions