Abstract: Let integer k ≥ 1, G be a graph of order n,n ≥ max {4k-6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G has a k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.