  Homotopy on nanophrases is an equivalence relation defined using some data
called a homotopy data triple. We define a product on homotopy data triples. We
show that any homotopy data triple can be factorized into a product of prime
homotopy data triples and this factorization is unique up to isomorphism and
order. If a homotopy data triple is composite, we show that equivalence of
nanophrases under the corresponding homotopy can be calculated just by using
the homotopies given by its prime factors.
