In this paper we consider two problems concerning string factorisation. Specifically given a string w and an integer k find a factorisation of w where each factor has length bounded by k and has the minimum (the FmD problem) or the maximum (the FMD problem) number of different factors. The FmD has been proved to be NP-hard even if k = 2 in [9] and for this case we provide a 3/2-approximation algorithm. The FMD problem, up to our knowledge has not been considered in the literature. We show that this problem is NP-hard for any k ≥ 3. In view of this we propose a 2-approximation algorithm (for any k) an exact exponential algorithm. We conclude with some open problems.