CMO 2001 Problem 4

Let $n$ be a positive integer. Nancy is given a rectangular table in which each entry is a positive integer. She is permitted to make either of the following two moves:

(1) select a row and multiply each entry in this row by $n$ ;

(2) select a column and subtract $n$ from each entry in this column.

Find all possible values of $n$ for which the following statement is true:

Given any rectangular table, it is possible for Nancy to perform a finite sequence of moves to create a table in which each entry is $0$ .