A k-regular spanning subgraph of G is called a k-factor of G. In this paper we give a necessary and sufficient condition for the inserted graph I(G) of a non-trivial graph G to have a 1-factor. If denotes the degree of the vertex v in G and if for all vertices v in G, where is an even integer then we prove that the inserted graph I(G) of G has a 2m-factor. Also we prove that if m is a non-negative integer and G is a connected graph with even number of edges such that for all vertices v in G, then the inserted graph I(G) of G has a -factor.