AMC 8 2017 Problem 19

For any positive integer $M$, the notation $M!$ denotes the product of the integers $1$ through $M$. What is the largest integer $n$ for which $5^n$ is a factor of the sum $98!+99!+100!$ ? $\textbf{(A) }23 \textbf{(B) }24 \textbf{(C) }25 \textbf{(D) }26 \textbf{(E) }27$