# Prime factorization: easiest way?

For prime factorization, is there another way of doing it, distinct from dividing the number by a series of primes (starting by the smallest)?

Couldn't we also pick the same series of primes and multiply them somehow until we got the target number?

It's clear that any approach will imply lots of computation, but some ways could be tougher than others, couldn't they?

Is there a name for an exploratory multiplication to try to reach a number?

I am specially interested in doing this with big numbers. It's clear that finding the prime factors of 24 or 32 is an easy task in both directions (dividing or multiplying). But with things like 598703019332, would it be feasible at all?

• mersenne.org/various/math.php (about Mersenne's primes) – Dunno Jan 30 '14 at 15:08
• For very small numbers, trial division actually is the best method. – Peter Jan 30 '14 at 15:10
• For 20 digit-numbers it is already cumbersome, and for, lets say, 80-digit numbers, it is unfeasible. There are much better methods for such numbers. – Peter Jan 30 '14 at 15:11
• Simply google for prime factorization to get a survey. – Peter Jan 30 '14 at 15:12
• Using all known methods a 100-digit-number can be factored in about one day! – Peter Jan 30 '14 at 15:14