SOLUTION: My mystery number only has the prime factors of 2,3, and 5. It has 18 factors. What are the possibilities for my mystery number?

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Question 1030289: My mystery number only has the prime factors of 2,3, and 5. It has 18 factors. What are the possibilities for my mystery number?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The mystery number would have the form 2%5Ep%5B1%5D%2A3%5Ep%5B2%5D%2A5%5Ep%5B3%5D. The number of factors, or divisors, is given by %28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29.
==> %28p%5B1%5D%2B1%29%28p%5B2%5D%2B1%29%28p%5B3%5D%2B1%29+=+18.
But 18 = 2*3*3, hence there are %283%21%29%2F%281%212%21%29+=+3 possibilities, namely
p%5B1%5D=1, p%5B2%5D=2, p%5B3%5D=2;
p%5B1%5D=2, p%5B2%5D=1, p%5B3%5D=2;
p%5B1%5D=2, p%5B2%5D=2, p%5B3%5D=1;
==> The possibilities for the mystery number are 450, 300, or 180.