Cycle factorizations of cycle products

Let n and k1,k2,…,kn be integers with n > 1 and ki ⩾ 2 for 1 ⩽ i ⩽ n. We show that there exists a Cs-factorization of Πi=1n C2ki if and only if s = 2t with 2 ⩽ t ⩽ k1 + ··· + kn. We also settle the problem of cycle factorizations of the d-cube.