1. Within a system comprising a processor and a memory, a method of determining a factorization permutation for a natural number, the method comprising: storing a canonical prime factor vector within the memory, wherein the canonical prime factor vector comprises unique prime factors of a prime factorization of the natural number; storing a first basis vector within the memory, wherein the first basis vector corresponds to the canonical prime factor vector and specifies a number of instances of each unique prime factor within the prime factorization; deriving a first count sequence, comprising a plurality of counts, from the first basis vector, wherein each count of the first count sequence is a child of the first basis vector; for each count of the first count sequence, outputting a second basis vector that is a child of the count, wherein each count of the first count sequence and child second basis vector specifies a factorization permutation of the natural number; determining, using the processor, an attribute of a circuit design defined by the factorization permutations; selecting at least one factorization permutation according to the attribute of the circuit design defined by the factorization permutations; and outputting the at least one factorization permutation.