<Li> Construct an ambiguous form (a, b, c) (\ displaystyle (a, b, c)) that is an element f ∈ G of order dividing 2 to obtain a coprime factorization of the largest odd divisor of Δ in which Δ = − 4 a c or a (a − 4 c) or (b − 2 a) (b + 2 a) (\ displaystyle \ Delta = - 4ac (\ text (or)) a (a-4c) (\ text (or)) (b - 2a) (b + 2a)) </Li> <Li> If the ambiguous form provides a factorization of n then stop, otherwise find another ambiguous form until the factorization of n is found . In order to prevent useless ambiguous forms from generating, build up the 2 - Sylow group Sll (Δ) of G (Δ). </Li> <P> To obtain an algorithm for factoring any positive integer, it is necessary to add a few steps to this algorithm such as trial division, and the Jacobi sum test . </P> <P> The algorithm as stated is a probabilistic algorithm as it makes random choices . Its expected running time is at most L n (1 2, 1 + o (1)) (\ displaystyle L_ (n) \ left ((\ tfrac (1) (2)), 1 + o (1) \ right)). </P>

Best algorithm to find factors of a number