  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.
