SOLUTION: What is the smallest positive integer with at least 100 positive integral factors?

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Question 955596: What is the smallest positive integer with at least 100 positive integral factors?
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
If a, b, c etc are unique primes, then the number has (a+1)(b+1)(c+1)... factors.

100 = 2^2 * 5^2 = (1+1)(4+1)

Pick the smallest primes: 2^4 * 3^4 * 5 * 7 = 45,360