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For how many positive integer values of $n$ is $3^n$ a factor of $15!$?

 Feb 12, 2021
 #1
avatar+18 
+1

We first determine the largest positive integer value of n such that 3^n | 15!. We determine this by counting the number of factors of 3 in the product. There are 5 multiples of 3 in the product, and there is one extra factor of 3 in 9, so there are a total of 5 + 1 = 6 factors of 3 in the product of the first 15 integers. So, for all n between 1 and 6, inclusive, 3^n is a factor of 15!
so it is 6

 Feb 12, 2021
edited by XxAngelGirlxX  Feb 12, 2021
 #2
avatar+116125 
+1

15!   =

 

1 * 2  * 3  *  4  * 5 * (2*3)  * 7 * 8 * (3 *3) * 10 * 11 * (4*3) * 13 * 14 * (5*3)   =

 

3 * 3 * 3 * 3 * 3 * 3  *  (all the rest)

 

 n  =  6 positive integer values

 

 

cool cool cool

 Feb 12, 2021

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