An atomic integral domain R is a half-factorial domain (HFD) if whenever $chi_1$… $chi_{m}=y_1$…$y_n$ with each $chi_{i},y_j in R$ irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then $Cl_{t}(R)$ $cong$ $Cl_{t}$(R[X]), and if $G_1$ and $G_2$ are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = $G_1igoplus; G_2$.