# Different positive factors of an integer

Find the smallest positive integer with exactly n different positive factors when n is:

3,4,5,6,10

I am not sure if I should do it like this:

For 3 the answer would be: 1 * 2 * 3 = 6 (or is 1 not counted? in that case 2 * 3 * 5 = 30)

By this approach for 6 the answer would be: 2 * 3 * 5 * 7 * 11 * 13?

Or maybe 1,2,3,4,6,12? So the answer would be 12?

I'm not sure how exactly to attack this problem.

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#### Solution Preview

In this question, we need to find the smallest positive integer with exactly n different positive factors. In fact, the more accurate statement is to find the smallest positive integer with n different prime numbers. 1 is a factor of every number but it ...

#### Solution Summary

This solution shows how to find the smallest positive integer with various specified numbers of positive factors.