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    Different positive factors of an integer

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    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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    https://brainmass.com/math/finite-element-method/different-positive-factors-integer-505052

    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.

    $2.19