I am not sure my explaination is 100% correct and it is base on the information I believe is probably correct.
The scale of 1/72, 1/48, 1/32 and 1/24 is base on old standard units(or British units) that is foot/inches. In fact these are sometimes used in architecture scale drawings. The reason is that in the pass, most vehicles were designed in a size with feet/inches as units. Now 1 foot equals to 12 inches( when you get 1/72, 1/48, 1/24 scale, 1 inche equals to 6ft, 4ft or 2ft respectively). On the other hand, 1 inch can be divided into 16 or 32 sections(see your ruler) and thus you get 1/16 or 1/32 or 1/96.
Scale like 1/50 and 1/100 are base on metric. That is the vehicle si measured in meters/cm etc. Obviously they are not popular.
The 1/35 scale is unique. I read an article from a model magazine 25 years ago in which the editor claimed he had an interview with Mr. Tamiya. Here is how the 1/35 comes from:
Sometime in the 1960's, Tamiya(?) wanted to developed a scale for it's FIGURES. Instead of selecting a scale, they first determine the end product of the figure should be 50mm(1.96 inche or 1&15/16 inch) tall. Tamiya then assumed the average man to be 5feet and 8.5 inches(1.74meter) tall. So, in order for a 1.74 meter tall man to become 50mm tall(or convert a 5' 8.5" man to 1.96 in.) we have to
shrink him into 35 times(actually it's 34.8, but round up).
This result the 1/35 scale. If you have some very old Tamiya figures, measure their height, they are very closed to 50mm. Therefore, the 1/35 scale for AFV is actually originally design for figures.
Well, this is what I head of, and I can't guarantee it's right but it seems convincing.