What is the largest exponent $k$ for which $3^{k}$ divides $100!$?

Step 1 of 3

1. 1.Legendre's formula sums $\left\lfloor \frac{100}{3^{i}} \right\rfloor$ over $i \ge 1$: each multiple of $9$ contributes a second factor $3$, each multiple of $27$ a third, and so on.