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How many positive divisors of 30! are prime?

 Jul 9, 2020
 #1
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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!.

 Jul 9, 2020
 #2
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Thank you!

Unicornrabbit  Jul 9, 2020
 #3
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this is why i love this forum, full of smart and respectful people!!

 Jul 9, 2020

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