Abstract: Let G be a group and A and B be subgroups of G. If G = AB, then G is said
to be factorized by A and B. Let p be a prime number. The factorization numbers of
a 2-generators abelian p-group and a modular p-group have been determined. Further,
suppose that G is a finite p-group as follows  G = <a,b|_apⁿ= _bp^m=1 , a^b = _apⁿ⁻¹⁺¹>, where n≥ 2, m≥ 1. In this paper, the factorization number of G is computed completely, which
is a generalization of the result of Saeedi and Farrokhi.

Key words: Finite p-group, Factorization number, Subgroup commutativity degree