Q. 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?

Explanation : 

Step 1: Restate the problem

We seek natural numbers N for which there exist three distinct divisors p, q, r of N satisfying

p + q + r = N.

Step 2: Change to reciprocal form

If p divides N, write p = N/a for some integer a≥1. Similarly q=N/b and r=N/c, with 1≤a<b<c. Then

p+q+r = N becomes

N·(1/a + 1/b + 1/c) = N

⇒ 1/a + 1/b + 1/c = 1.

Step 3: Solve 1/a + 1/b + 1/c = 1 in distinct positive integers

By testing small denominators (or using known Egyptian‐fraction results), the only solution with a<b<c is

a=2, b=3, c=6

because 1/2 + 1/3 + 1/6 = 1.

Step 4: Translate back to p, q, r

From (a,b,c)=(2,3,6) we get

p = N/2, q = N/3, r = N/6.

These are three distinct divisors of N exactly when 6 divides N, and they indeed satisfy p+q+r=N.

Step 5: Count all such N < 50

The positive multiples of 6 below 50 are

6, 12, 18, 24, 30, 36, 42, 48 — a total of 8 numbers.

Therefore, the answer is (c) 8.