2024 Fermat Problem 16

Francesca put one of the integers 1, 2, 3, 4, 5, 6, 7, 8, 9 in each of the nine squares of the grid shown. No integer is used twice. She calculated the product of the three integers in each row and wrote the products to the right of the corresponding rows. She calculated the product of the integers in each column and wrote the products below the corresponding columns. Finally, she erased the integers from the nine squares. Which integer was in the square marked N?

\begin{array}{|c|c|c|c}\hline \phantom{00} & \phantom{00} & \phantom{00} & 56 \\ \hline \phantom{00} & \phantom{00} & \phantom{00} & 135 \\ \hline \phantom{00} & N & \phantom{00} & 48 \\ \hline 21 & 108 & 160 & \end{array}

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 8\quad \textbf{(E)}\ 9

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 Fermat contests here.