AMC 10 2021-fall-b Problem 8

The greatest prime number that is a divisor of $16{,}384$ is $2$ because $16{,}384 = 2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of $16{,}383$? $\textbf{(A)} \: 3 \textbf{(B)} \: 7 \textbf{(C)} \: 10 \textbf{(D)} \: 16 \textbf{(E)} \: 22$