When representing two numbers by their numerals in positional notation, e.g. $720$ and $721$, it is easy to decide which of the numbers is greater by comparing their digits from left to right. Alternatively, every natural number can be uniquely identified by its prime factorization. So I'm wondering whether it's possible to decide which number is greater by considering the two prime factorizations (without multiplying the prime factors to get back the original numbers). E.g. $\{2,2,2,2,3,3,5\}$ and $\{7,103\}$.
2026-04-01 08:06:46.1775030806
Given the prime factors of two natural numbers, is it possible to decide which of the numbers is greater?
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