3. Given that a triangle can be divided into $N$ similar quadrilaterals. Find all possible values of the positive integer $N$.


3. Obviously, $N \neq 1$.
$N=2$ is also impossible. This is because if a triangle is divided into two quadrilaterals, one must be a convex quadrilateral and the other a concave quadrilateral.

As shown in Figure 11, for $N=3$, a division that meets the problem's requirements can be made in an equilateral triangle.

For $N \geqslant 3$, a division that meets the problem's requirements can also be made in an equilateral triangle through inductive construction, as shown in Figure 12.