2013 AMC 8 Problem 17

The sum of six consecutive positive integers is 2013. What is the largest of these six integers?

\textbf{(A)}\ 335 \qquad \textbf{(B)}\ 338 \qquad \textbf{(C)}\ 340 \qquad \textbf{(D)}\ 345 \qquad \textbf{(E)}\ 350

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