2024 Gauss 8 Problem 23

Five *different* integers, each greater than 0, have a sum of 264. The greatest common divisor of these five positive integers is d. What is the sum of the digits of the largest possible value of d?

\textbf{(A)}\ 4\quad \textbf{(B)}\ 3\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 2\quad \textbf{(E)}\ 6

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