We show that if m ⩾ 2 is an even integer and G is a graph such that dG(v) ⩾ m + 1 for all vertices v in G, then the line graph L(G) of G has a 2m-factor; and that if m is a nonnegative integer and G is a connected graph with |E(G)| even such that dG(v) ⩾ m + 2 for all vertices v in G, then the line graph L(G) has a (2m+1)-factor.