In this paper, firstly, we give some characterizations of simply sm-factorizable (para)topological groups by continuous real-valued functions. It mainly shows that G is a simply sm-factorizable (para)topological group if and only if, for each continuous function f : G → R, there are a sub-sm-(para)topological group H, a continuous homomorphism h of G onto H and a continuous function g :Secondly, applying those results we study the completions of simply sm-factorizable topological groups. We prove that the equalities µG = ̺ω(G) = υG hold for each Hausdorff simply sm-factorizable topological group G. This result gives a positive answer to a question posed by Arhangel'shiǐ and Tkachenko [2, Problem 7.6]. Finally, we discuss the realcompactification of simply sm-factorizable paratopological groups. We mainly, among other results, the realcompactification υG of a regular simply smfactorizable paratopological group admits a natural structure of paratopological group containing G as a dense subgroup and υG is also simply sm-factorizable. Some results in [12] are improved.2010 Mathematics Subject Classification. 22A05, 22A30,54H11, 54A25, 54C30.