What is the greatest positive integer \(n\) such that \(3^n\)is a factor of \(200!\)?
\(\text{The total powers of }3 \text{ in }200! \text{ are}\\ \left\lfloor \dfrac{200}{3}\right\rfloor + \left\lfloor \dfrac{200}{9}\right\rfloor + \left\lfloor \dfrac{200}{27}\right\rfloor + \left\lfloor \dfrac{200}{81}\right\rfloor =97\)
