What is the largest integer n such that 3^{n} is a factor of 1 x 3 x 5 x... x 97 x 99?

Guest Feb 16, 2020

#1**+1 **

We can use Legendre's formula: https://en.wikipedia.org/wiki/Legendre%27s_formula

By Legendre's formula, the number of factors of 3 is

\(\left\lfloor \frac{99}{3} \right\rfloor + \left\lfloor \frac{99}{3^2} \right\rfloor + \left\lfloor \frac{99}{3^3} \right\rfloor + \left\lfloor \frac{99}{3^4} \right\rfloor = 33 + 11 + 3 + 1 = 48\)

.Guest Feb 16, 2020