N as sum of three distinct factors below 50

Divide the given equation N = p + q + r by N to get: 1 = p/N + q/N + r/N. Since p, q, r are factors of N, the fractions N/p, N/q, N/r must be distinct integers. Let's call them P, Q, R. We get 1 = 1/P + 1/Q + 1/R. The only solution to this equation with distinct positive integers is 1 = 1/2 + 1/3 + 1/6. This means the factors must be ⟨MATH⟩N/2, N/3, N/6⟨/MATH⟩. For these to be integers, ⟨MATH⟩N⟨/MATH⟩ must be a multiple of 6. The multiples of 6 strictly less than 50 are: 6, 12, 18, 24, 30, 36, 42, 48. There are 8 such numbers.

Answer: (c).