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Let $N$ be a natural number.

How to find decomposition of $N = a b c$ where $a, b, c$ are "maximal" natural numbers. It means that deviation of these numbers from each other is minimal.

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    is it true that any such algorithm has complexity $\mathcal{O}(n^3)$? – 2017-01-03
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    It is interesting question. Unfortunately I don't know lower bound of optimal algorithm's complexity – 2017-01-03
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    This problem must be at least as hard as integer factorization, for which it is not known whether it is in $P$ – 2017-01-03
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    It seems to me you are asking for a variant factorization algorithm to [Fermat's factorization method](https://en.wikipedia.org/wiki/Fermat's_factorization_method), but searching in the vicinity of $\sqrt[3]{N}$ rather than $\sqrt{N}$. – 2017-01-03
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    While the premise of your Question seems intriguing, it is not precisely formulated. Compare the way you've asked this to this [previous Question about integer factorization](http://math.stackexchange.com/questions/631559/algorithms-for-finding-the-prime-factorization-of-an-integer) and try to appreciate the handicap for Readers imposed by your Question's lack of context. – 2017-01-05
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    You have visited the site without clarifying the intent of this Question. Among other problems the assumptions are not stated precisely -- is $N$ known to have three nearly equal factors, or do you ask to determine whether this is the case? Do you ask to find three factors as nearly equal as possible, as [this SO Question does](http://stackoverflow.com/questions/28057307/factoring-a-number-into-roughly-equal-factors)? If so, are you assuming a prime factorization of $N$ is given? – 2017-01-05
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    @hardmath, this question resembles mine. Yes, I meant to find three factors as nearly equal as possible. – 2017-01-05
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    Have you already obtained a prime factorization of $N$? – 2017-01-05
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    As I understood the key idea is to perform prime factorization then merge prime numbers by multiplying? – 2017-01-05

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