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What is the greatest positive integer \(n\) such that \(3^n\)is a factor of \(200!\)?

 Jan 13, 2019

Best Answer 

 #1
avatar+4033 
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\(\text{The total powers of }3 \text{ in }200! \text{ are}\\ \left\lfloor \dfrac{200}{3}\right\rfloor + \left\lfloor \dfrac{200}{9}\right\rfloor + \left\lfloor \dfrac{200}{27}\right\rfloor + \left\lfloor \dfrac{200}{81}\right\rfloor =97\)

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 Jan 13, 2019
 #1
avatar+4033 
+2
Best Answer

\(\text{The total powers of }3 \text{ in }200! \text{ are}\\ \left\lfloor \dfrac{200}{3}\right\rfloor + \left\lfloor \dfrac{200}{9}\right\rfloor + \left\lfloor \dfrac{200}{27}\right\rfloor + \left\lfloor \dfrac{200}{81}\right\rfloor =97\)

Rom Jan 13, 2019

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