Physics of Factorization
  The N distinct prime numbers that make up a composite number M allow $2^{N-1}$ bi partioning into two relatively prime factors. Each such pair defines a pair of conjugate representations. These pairs of conjugate representations, each of which spans the M dimensional space are the familiar complete sets of Zak transforms (J. Zak, Phys. Rev. Let.{\bf 19}, 1385 (1967)) which are the most natural representations for periodic systems. Here we show their relevance to factorizations. An example is provided for the manifestation of the factorization. 
M. Revzen, A. Mann and J. Zak