  In this paper by using the path integral formulation of the background field
method of QCD in the presence of SU(3) pure gauge background field we
simultaneously prove the renormalization of ultra violet (UV) divergences and
the factorization of infrared (IR) and collinear divergences in QCD at all
orders in coupling constant. We prove that although perturbative QCD is
renormalizable but due to confinement in QCD it is not necessary to renormalize
QCD to study hadrons production at high energy colliders. This is consistent
with the fact that the partons are not directly experimentally observed but the
hadrons are directly experimentally observed.
