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Torsion-free part of the unit group of ZC 24 is generated by 5 units. In this paper, we firstly will give a parametrization of torsion-free units in ZC 24 and later we shall characterize the unit group of ZC 24 by using some ring extensions. Mathematics Subject Classification: 16S34, 16U60doi:10.12988/ija.2014.4555 fatcat:tcpjrsefvzdsvoikg7zbkng54u