text: An atomic monoid is length-factorial if each two distinct factorizations of any element have distinct factorization lengths. We provide a characterization of length-factorial Krull monoids in terms of their class groups and the distribution of prime divisors in the classes.
  Acknowledgements
  This work was supported by the Austrian Science Fund FWF, Project P33499-N and by the National Natural Science Foundation of China, Grant No. 12001331.