An edge-colouring of a graph G is equitable if, for each vertex v of G, the number of edges of any one colour incident with v di ers from the number of edges of any other colour incident with v by at most one. Hilton and de Werra have proved that if k does not divide d(v) for all vertex v ∈ V (G), then G has an equitable edge-colouring with k colours. In this paper, using the result of Hilton and de Werra, we give the very simple proofs of several results on f-edge colourings and f-edge cover colourings the original proofs of which are diffcult. Furthermore, we give some new sharp su cient conditions for a graph to have (g, f)-factorizations which improve the results in [8].