Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n− 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most (n− 3)/(δ − 1) components, unless G is...