Explanation:

Any number of the form p^aq^br^c will have (a + 1) (b + 1)(c + 1) factors, where p, q, r are prime. (This is a very important idea)
For any number N of the form p^aq^br^c, the sum of the factors will (1+p¹+p²+…+p^a)(1+q¹+q²+…+q^b) (1+r¹+r²+…+r^c)
Sum of factors of number N is 124. 124 can be factorized as 22 × 31. It can be written as 4 × 31, or 2 × 62 or 1 × 124.
2 cannot be written as (1+p¹+p²+…+p^a) for any value of p.
4 can be written as (1 + 3)
So, we need to see if 31 can be written in that form.
The interesting bit here is that 31 can be written in two different ways.
= 31= (1+2¹+2²+2³+2⁴)
= 31= (1+5+5²)
Or, the number N can be 3×2⁴ or 3×5². Or N can be 48 or 75.
So, more than one such number exists.