2017 AMC 8 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\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.