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Until now, the two-dimensional ferromagnets remain mostly limited to exfoliated micron-sized samples. Large-scale thin films are desirable for the fabrication of integrated devices for spintronic and memory storage applications. Among this group of materials, Fe₃GeTe₂ (FGT) can host ferromagnetic states at room temperature upon optimized gating. We achieve, by molecular beam epitaxy, the synthesis of high-quality monolayer and multilayer FGT films. Surface x-ray diffraction confirms its quintuple layer substructures with hexagonal symmetry. Thickness-dependent transport measurements are used to probe and characterize magnetic order. Ferromagnetic states exist in 1-10 layer thick Fe₃GeTe₂, with Curie temperatures ranging from ~75 K in one layer samples to above 175 K in ten layer samples. A ferromagnetic phase with significant magnetic anisotropy is revealed for all layer numbers.