  Factorization in algebra is an important problem. In this paper, we first
obtain a unique factorization in free Nijenhuis algebras. By using of this
unique factorization, we then define a coproduct and a left counital
bialgebraic structure on a free Nijenhuis algebra. Finally, we prove that this
left counital bialgebra is connected and hence obtain a left counital Hopf
algebra on a free Nijenhuis algebra.
