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).
2 by 150
3 by 100
4 by 75
5 by 60
6 by 50
10 by 30
12 by 25
15 by 20
and vice versa