What Does A Number Look Like?

Very recently I came across a site called Numbermatics that provides information about the properties of an entered number but also represents the number pictorially in terms of its prime factors and number of divisors. The home page asks the question: What does the number 43003166792914270 look like? This is response:

As the fine print above says: the visualisation shows the ratios of its 4 prime factors (large circles) and 24 divisors. The only problem is that 43003166792914270 has six prime factors and not four, an inauspicious introduction to a website. The factorisation is 2 * 5 * 191 * 3533 * 5119 * 1244911. 

However, entering the same number into the search box brings up the correct factors and representation:

I've sent an email informing the site of of its error. Anyway, back to the pictorial representation, my reaction is mixed. The overlapping circles in the centre, representing the prime factors, overlap one another which immediately reminded me of Venn diagrams and intersection of sets. To my mind, the circles should not overlap, as the factors having nothing in common, and the area of the circle should be proportional to the size of the factor. Maybe the idea is that the prime factors are like the nucleus of an atom and the divisors are like the electrons in orbit around it. 

If so, then this idea would work better in 3 dimensions where spheres could represent the prime factors, be clearly separate and have their volumes proportional to the size of the factors. The various combinations of factors could represent the various electron shells: the inner shell would consist of factors formed by combining two prime factors, the next shell would consist of factors formed by combining three prime factors and so on. This is overly ambitious I'm sure and to be fair the Numbermatics representation looks good and conveys the information clearly once you understand how it works.

If the factors 2 * 5 * 191 * 3533 * 5119 * 1244911 were represented as spheres then the corresponding radii of these spheres would be 1.3, 1.7, 5.8, 15.2, 17.2 and 107.6 (to one decimal place). This means that while the largest factor (1244911) is 622455.5 larger than the smallest factor (2), the radius of the largest sphere is only a little more than 85 times the radius of the smallest sphere. The composite factors could be similarly represented and would tend to grow in volume as the number of prime factor constituents increased.