Key idea: If $N$ is a multiple of 6, then the three distinct proper factors $p = N/6$, $q = N/3$, $r = N/2$ satisfy $p + q + r = N$ and are all factors of $N$.

Hence, every multiple of 6 works. Below 50, the multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48 → 8 numbers.

Therefore, the required count is 8.