LetRbe a commutative ring andA↦Mm×n. The spanning rank ofAis the smallest positive integersfor whichA=PQ(m×ss×n) The spanning rank of the zero matrix is set equal to zero. IfRis a field, then the spanning rank ofAis just the classical rank ofA. In the first section of this paper, various theorems and examples are given which indicate how much of the classical theory of rank is still valid for spanning rank over a commutative ring. IfA=PQ(n×ss×n) is a spanning rank factorization of a square matrix andD=QP, thenDis called a spanning rank partner ofA. In the second part of this paper, the null idealsNAandNDofAandDrespectively are compared. For instance, we showNA=NDifs=nandNA=XNDifs<nwheneverRis aPIDandA≠0. This result sometimes (e.g.s<<n) makes the computation ofNAeasy.