There is the arithmetic mean/geometric mean inequality that will show for positive real numbers that the maximum product is no larger than (S/n)^n where S is the sum of the numbers (matching your (100/n)^n). (Google will find this.) The proof for that inequality might suggest a way to go.

Yes, they should all be the same, that is, when they are integers. For 2 numbers, you'll have 50 and 50 and for three, it'll be 100/3 each. Then it seems logical to me, that for n numbers, the formula to calculate the product, is (100/n)^n The maximum value for n turns out te be 37 and the corresponding maximum product 9.474*10^15 But....that's only if n can be real valued.

If n can only be an integer, I think the maximum product should be 3^32*2^2, so I used 32 three's and 2 two's. But is that for sure and how can I check that? I think I should use something like number theory as well., but have no idea how...