2019 Cayley Problem 25

For how many positive integers x does there exist a rectangular prism PQRSTUVW, labelled as shown, with PR = 1867, PV = 2019, and PT = x?

\textbf{(A)}\ 1980\quad \textbf{(B)}\ 1982\quad \textbf{(C)}\ 1984\quad \textbf{(D)}\ 1983\quad \textbf{(E)}\ 1981

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.