Using Single Time of Quantum Computer for Shor's Factoring Algorithm

Peter Shor's in 1994 developed a factoring algorithm that can factor a composite number
$\boldsymbol{n}$
in a polynomial time by using a quantum computer in one step of the algorithm. The algorithm may contain a loop that requires calling a quantum computer many times to find the order of selected number
$a, a\in Z_{n}$
. In this paper, the improvement to the Shor's factoring algorithm guarantees the single use of the quantum computer to find the order, where the rest of the algorithm can be implemented by a classical computer. A numerical example for the original and improved version is presented.