In [[number theory]], a '''multiplicative partition''' or '''unordered factorization''' of an integer ''n'' that is greater than 1 is a way of writing ''n'' as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the termsfactors. The number ''n'' is itself considered one of these products. Multiplicative partitions closely parallel the study of '''multipartite partitions''', discussed in {{harvtxt|Andrews|1976}}, which are additive [[partition]]s of finite sequences of positive integers, with the addition made [[pointwise]]. Although the study of multiplicative partitions has been ongoing since at least 1923, the name "multiplicative partition" appears to have been introduced by {{harvtxt|Hughes|Shallit|1983}}. The Latin name "factorisatio numerorum" had been used previously. [[MathWorld]] uses the name '''unordered factorization'''.
