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Optimizing the use of grid resources is critical for users to effectively exploit a Data Grid (DG). Data replication is considered as a major technique for increasing access performance and data availability in DG systems. Current works on data replications in Grid systems focuses on infrastructure for replication mechanism for creating or deleting replicas. One of the challenges in data replication is determining Optimal Number of Replicas (ONR) with Quality of Service (QoS) assurance, as well as their Optimal Location of Replicas (OLR) in DG. In this paper, we propose an algorithm that finds ONR of an object over DG systems, such that the overall communication and storage cost is minimized. This algorithm ensures that QoS required from the users are satisfied. In addition, we proposed a sketch of the proof for our algorithm and its integrity.