+781 I'm sure there's a more clever way than this. Anyways:
We write the prime factorization of 30! to get 2^26×3^14×5^7×7^4×11^2×13^2×17×19×23×29 (using Wolfram Alpha). The prime factors here are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So there are 10 prime divisors of 30!.
+773 this is why i love this forum, full of smart and respectful people!!
