  We study the behavior with the number of colors ($N_c$) of the
$\Lambda(1405)$ and $\Lambda(1670)$ resonances obtained dynamically within the
chiral unitary approach. The leading order meson-baryon interaction, used as
the kernel of the unitarization procedure, manifests a nontrivial $N_c$
dependence of the flavor SU(3) representation for baryons. As a consequence,
the SU(3) singlet (or $\bar{K}N$) component of the $\Lambda(1405)$ states
remains bound in the large $N_c$ limit, while the other components dissolve
into the continuum. Introducing explicit SU(3) breaking, we obtain the $N_c$
dependence of the excitation energy, masses and widths of the physical
$\Lambda(1405)$ and $\Lambda(1670)$ resonance. The $N_c$ behavior of the decay
width is found to be different from the general counting rule for a $qqq$
state, indicating the dynamical origin of these resonances.
