2006 Gauss 8 Problem 24

In the diagram, the grid has 150 rows and 150 columns, numbered from 1 to 150. In row 1, every box is shaded. In row 2, every second box is shaded. In row 3, every third box is shaded. The shading continues in this way, so that every nth box in row n is shaded. Which *column* has the greatest number of shaded boxes?

\textbf{(A)}\ 144\quad \textbf{(B)}\ 120\quad \textbf{(C)}\ 150\quad \textbf{(D)}\ 96\quad \textbf{(E)}\ 100

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 Gauss contests here.