I'm looking for an algorithm that returns true if the set of prime factors of some number only contains values in some set $S$, and false otherwise
Example:
$S = \{2,5\}$
For the number $250$ the result is true, since the prime divisors are $2*5^3$
For the number $182$ the result is false, since the prime divisors are $2*7*13$
Since I don't need the actual divisors, I'm hoping there's a faster method than just factoring the number.