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.