  After extending the theory of Rankin-Selberg local factors to pairs of
$\ell$-modular representations of Whittaker type, of general linear groups over
a non-archimedean local field, we study the reduction modulo $\ell$ of
$\ell$-adic local factors and their relation to these $\ell$-modular local
factors. While the $\ell$-modular local $\gamma$-factor we associate to such a
pair turns out to always coincide with the reduction modulo $\ell$ of the
$\ell$-adic $\gamma$-factor of any Whittaker lifts of this pair, the local
$L$-factor exhibits a more interesting behaviour; always dividing the reduction
modulo-$\ell$ of the $\ell$-adic $L$-factor of any Whittaker lifts, but with
the possibility of a strict division occurring. In our main results, we
completely describe $\ell$-modular $L$-factors in the generic case. We obtain
two simple to state nice formulae: Let $\pi,\pi'$ be generic $\ell$-modular
representations; then, writing $\pi_b,\pi'_b$ for their banal parts, we have
\[L(X,\pi,\pi')=L(X,\pi_b,\pi_b').\] Using this formula, we obtain the
inductivity relations for local factors of generic representations. Secondly,
we show that \[L(X,\pi,\pi')=\mathbf{GCD}(r_{\ell}(L(X,\tau,\tau'))),\] where
the divisor is over all integral generic $\ell$-adic representations $\tau$ and
$\tau'$ which contain $\pi$ and $\pi'$, respectively, as subquotients after
reduction modulo $\ell$.
