A natural number N is such that it can be expressed as N = p + q + r , where p, q and r are distinct factors of N. How many numbers below 50 have this property?

To solve this, we are looking for numbers where N is the sum of three of its distinct factors. Let the factors be p, q, and r. If we divide both sides of the equation N = p + q + r by N, we get 1 = p/N + q/N + r/N.

Since p, q, and r are factors of N, the fractions p/N, q/N, and r/N must be unit fractions like 1/2, 1/3, 1/4, etc. We need to find three distinct unit fractions that add up to 1. The only set of three distinct unit fractions that sum to 1 is 1/2 + 1/3 + 1/6.

This means that for N to satisfy the condition, its three factors must be N/2, N/3, and N/6. For these to be integers, N must be a multiple of the least common multiple of 2, 3, and 6, which is 6.

Therefore, any number that is a multiple of 6 will satisfy this property because N/2 + N/3 + N/6 = (3N + 2N + N) / 6 = 6N / 6 = N.

The multiples of 6 below 50 are 6, 12, 18, 24, 30, 36, 42, and 48. Counting these, we find there are exactly 8 such numbers. Thus, the correct option is C.