Whose camp are you in?

Probability Level 4

40 students attended the brilliant summer camp at Stanford University. kk of the students at the camp are working on math problems and the others are working on non-math problems. One of the camp mentors noticed that whenever all the students were partitioned into 2 or more groups of equal size, they could never have the same number of math students in every group. How many different values could kk have?

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