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

Guest Jan 13, 2019

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

Rom Jan 13, 2019

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Rom · Answer 1 · 2019-01-13T11:00:08

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

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