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Is finding the largest prime factor of a number computationally easier than factoring the number into powers of primes?

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this is an offshoot of the 3rd problem on ProjectEuler. –  ajay Sep 25 '12 at 5:56
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If the largest prime factor can be found in polynomial time, then applying the same algorithm a linear number of times produces a complete prime factorization, still in polynomial time. So, no, it's not easier. –  mjqxxxx Sep 25 '12 at 6:03
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