  Let $ABC$ be an equilateral triangle. For certain triangles $T$ (the "tile")
and certain $N$, it is possible to cut $ABC$ into $N$ copies of $T$. It is
known that only certain shapes of $T$ are possible, but until now very little
was known about the possible values of $N$. Here we prove that for $N>3$, $N$
cannot be prime, and study more closely the possible tilings when the tile has
a $\pi/3$ angle.
