Germanium cantilever nanoelectromechanical resonators were fabricated using chemically grown nanowires with diameters ranging from 50 to 140 nm. Single nanowires were mechanically positioned at the edge of a copper transmission electron microscope (TEM) grid and then pinned to the grid with local platinum deposition. Oscillating cantilevers were induced into electromechanical resonance with an applied AC voltage, and the frequency response of the vibrational amplitude was measured. From this data, the Young's modulus of the nanowires was determined to be insensitive to diameter in this size range with an average value of 106 GPa (with 95% confidence limits of +/- 19 GPa), which is on par with the literature values for bulk Ge (100-150 GPa). The mechanical quality factors (Q) of the nanowire cantilevers were also measured and found to decrease with decreasing diameter. The data indicate that energy dissipation from the oscillating cantilevers occurs predominantly via surface losses, which increase in magnitude with increasing surface area-to-volume ratio of the nanowires.