2005 AMC 10A Problems/Problem 21
For how many positive integers does evenly divide ?
So the problem asks us for how many positive integers is an integer.
is an integer when is a factor of .
The factors of are , , , , , and .
So the possible values of are , , , , , and .
But isn't a positive integer, so only , , , , and are possible values of .
Therefore the number of possible values of is