Graphene is an important nanomaterial with extraordinary properties. An established physical vapor deposition (PVD) based Graphene synthesis method is engineered in order to demonstrate the versatility of the growth method with respect to the quality and number of layers of synthesized Graphene. A statistical method known as factorial Design-of-Experiments (DoE) is demonstrated in this paper to determine key factors for synthesis of Graphene on Copper (Cu) using amorphous carbon (a-C) as the solid carbon source. Both qualitative and quantitative analysis are performed to determine a suitable recipe. Carbon source thickness (which is a-C) annealing temperature and annealing duration are varied to study their effect on the growth. Annealing temperature and a-C thickness are found to be significant factors for growth feasibility in a PVD-based growth, whereas annealing time is found to play a crucial role in growing different number of layers of Graphene with different quality. The quality and number of layers of Graphene are verified by Raman characterization.