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  • I do agree that factorization by brute-force trying out all possible factors would take too long. But that does not mean that more clever algorithms are not possible (this is even true without thinking about quantum computers). As an example consider the problem of finding out if a given number N is or is not a prime number. If N is, say, a 1000 digit number one could also think that this is an impossible task, but in fact this can be done on ordinary computers, see en.wikipedia.org/wiki/Primality_test The test is just more complicated than trying out every possible divisor. Commented Jun 29, 2020 at 9:39