# Sam's Gym Dilemma

**Discrete Mathematics**Level 3

There are 300 students at a local high school. On "All Students Exercise Day", Sam, the Physical Education instructor, wants them to line up in a perfect rectangular formation (same number of students in each row). However, there must be more than 1 student in each row or column. How many different formations are there?

**Details and assumptions**

For this question, the students are considered identical.

A formation is different if there are a different number of rows. In particular, the 1 by 300 formation is different from the 300 by 1 formation (though neither are valid).