  We try to minimize the number of qubits needed to factor an integer of n bits
using Shor's algorithm on a quantum computer. We introduce a circuit which uses
2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to
implement the factorization algorithm. The circuit is computable in polynomial
time on a classical computer and is completely general as it does not rely on
any property of the number to be factored.
  Keywords: Factorization, quantum circuits, modular arithmetics
