Many algorithms have been devised for determining the prime factors of a given number (a process called
prime factorization). They vary quite a bit
in sophistication and complexity. It is very difficult to build a general-purpose
algorithm for this computationally "hard" problem, so any additional information
that is known about the number in question or its factors can often be used to save
a large amount of time.
The simplest method of finding factors is so-called "direct search factorization" (a.k.a. trial division).
In this method, all possible factors are systematically tested using trial division
to see if they actually divide the given number. It is
practical only for very small numbers.
The fastest-known fully proven deterministic algorithm is the Pollard-Strassen method
(Pomerance 1982; Hardy et al. 1990).
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Algorithms." In Discrete
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