A. What is the lowest number that has exactly 10 distinct positive factors?

B. Exactly 1,000 distinct positive factors?

C. Exactly 1,000,000 distinct positive factors?

Example: The distinct factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Thus 72 has 12 distinct factors.

I believe part A is 48.  I believe part B and C are for the computer.  Which makes them not for me.  Although I would like to see someone who could do one or both without a computer and some sort of mathematical proof or something.  I believe 48 is the lowest, although I have not tried them all below 48.  I have to do it manually on paper.

Posted by john on 2005-07-08 15:36:33