Create a set of prime factor numbers given a set of tuples

Given a set $$\Omega$$ of tuples, for example,

Tuples[{Range[0, 4], Range[0, 3], Range[0, 2]}]


how can I create all numbers on the form $$p_1^{t_1}p_2^{t_2}p_3^{t_3}$$ where $$p_i$$ are (prime) numbers and $$(t_1,t_2,t_3)\in\Omega$$? (This will give all possible dividers of $$p_1^4p_2^3p_3^2$$.)

It could be done with a basic For loop and splitting the elements into parts etc. but there must be a shorter, better and (much) smarter way to do it. TIA.

• Why not just use Divisors[p1^4 * p2^3 * p3^2] ? Jul 28 '20 at 14:02
• (Times @@ ({p1, p2, p3}^#)) & /@ Tuples[{Range[0, 4], Range[0, 3], Range[0, 2]}] Jul 28 '20 at 14:09
• #1. I did not know of this function. Thank you for solutions.
– mf67
Jul 28 '20 at 15:10