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How many different primes appear in the prime factorization of  $20!/18!$? (Reminder: The number n! is the product of the integers from 1 to  n. For example 5! = 5*4*3*2*1 = 120)

 Aug 29, 2021
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20! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , 19 , Total Prime Factors = 36
Distinct Number of Factors = 8

 

 

18! ==2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 3 , 5 , 5 , 5 , 7 , 7 , 11 , 13 , 17 , Total Prime Factors = 32
Distinct Number of Factors = 7

 

 

20! / 18! ==2 , 2 , 5 , 19 , Total Prime Factors = 4
Distinct Number of Factors = 3

 Aug 29, 2021

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