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How many different primes appear in the prime factorization of 20!

 Apr 6, 2020
 #1
avatar+538 
+2

8.

A prime number will only come up in the factorization of a factorial if the prime is less than n, with n being (n)!. THere are 8 primes less than 20- 2, 3, 5, 7, 11, 13, 17, and 19.

 

smileysmileysmiley

 Apr 6, 2020
 #2
avatar+274 
+1

That's great, you rock!

 Apr 6, 2020
 #3
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+1

20! = 2^18 * 3^8 * 5^4 * 7^2 * 11 * 13 * 17 * 19

 Apr 6, 2020

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