Vietnamese snake puzzle - Closed

[Gerson W. Barbosa]

I've found one solution using paper and pencil only, but I'm not pleased with my work. I assumed all intermediate results are integer. This implies c = 1, because 13 is prime. I didn't figure out any other way than atributing values to three variables (i, b and e) and changing them sequentially as they proved to be impossible. It took no more than an hour and a sheet of paper to find the solution, but that would be too much during an examination though.

No spoiler:

a.b.d.e = 120
f.g.h.i = 3024