  In this paper, we consider infinite words that arise as fixed points of
primitive substitutions on a finite alphabet and finite colorings of their
factors. Any such infinite word exhibits a "hierarchal structure" that will
allow us to define, under the additional condition of strong recognizability,
certain remarkable finite colorings of its factors. In particular, we
generalize two combinatorial results by Justin and Pirillo concerning
arbitrarily large monochromatic $k$-powers occurring in infinite words, in view
of a recent paper by de Luca, Pribavkina and Zamboni, we will give new examples
of classes of infinite words $\mathbf{u}$ and finite colorings that do not
allow infinite monochromatic factorizations
$\mathbf{u}=\mathbf{u}_1\mathbf{u}_2\mathbf{u}_3\ldots$.
