2. Find all positive integers $n$, such that all positive divisors of $n$ can be placed in the cells of a rectangular grid, satisfying the following constraints:
(1) Each cell contains a different divisor;
(2) The sum of the numbers in each row of cells is equal;
(3) The sum of the numbers in each column of cells is equal.
2. $n=1$.

Assume all positive divisors of $n$ can be placed in a $k \times l$ $(k \leqslant l)$ rectangular grid, and satisfy the conditions.
Let the sum of the numbers in each column of the grid be $s$.
Since $n$ is one of the numbers in a column of the grid, we have $s \geqslant n$, and the equality holds if and only if $n=1$.

For $j=1,2, \cdots, l$, let $d_{j}$ be the largest number in the $j$-th column of the grid. Without loss of generality, assume
$d_{1}>d_{2}>\cdots>d_{l}$.
Since $d_{1}, d_{2}, \cdots, d_{l}$ are all positive divisors of $n$, then
$d_{l} \leqslant \frac{n}{l}$.
And $d_{l}$ is the largest number in the $l$-th column of the grid, so
$d_{l} \geqslant \frac{s}{k} \geqslant \frac{n}{k}$.
From equations (1) and (2), we get $\frac{n}{l} \geqslant \frac{n}{k} \Rightarrow k \geqslant l$.
Thus, $k=l$.
Therefore, the equalities in equations (1) and (2) both hold.
In particular, we have $s=n$.
Hence, $n=1$, and $n=1$ satisfies the conditions.