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Understanding the correlation between magnetomechanical coupling factors (<i>k</i>) and damping factors (<i>Q⁻</i>¹) is a key pathway toward enhancing the magnetomechanical power conversion efficiency in laminated magnetoelectric (ME) composites by manipulating the magnetic and mechanical properties of Fe-based amorphous metals through engineering. The <i>k</i> and <i>Q⁻</i>¹ factors of FeSiB amorphous ribbons annealed in air at different temperatures are investigated. It is found that <i>k</i> and <i>Q⁻</i>¹ factors are affected by both magnetic and elastic properties. The magnetic and elastic properties are characterized in terms of the magnetomechanical power efficiency for low-temperature annealing. The <i>k</i> and <i>Q⁻</i>¹ of FeSiB-based epoxied laminates with different stacking numbers show that a −3 dB bandwidth and Young’s modulus are expressed in terms of the magnetomechanical power efficiency for high lamination stacking.