  We work out the factorization of the 3d superconformal index for N = 2
$U(N_c)$ gauge theory withone adjoint chiral multiplet as well as $N_f$
fundamental, $N_a$ anti-fundamental chiral multiplets. Using the
factorization,one can prove the Seiberg-like duality for N = 4 $U(N_c)$ theory
with $N_f$ hypermultiplets at the index level. We explicitlyshow that monopole
operators violating unitarity bound in a bad theory are mapped to free
hypermultiplets in the dual side. For N = 2 $U(N_c)$ theory with one adjoint
matter $X$, $N_f$ fundamental, $N_a$ anti-fundamental chiral multiplets with
superpotential $W = tr X^{n+1}$, we work out Seiberg-like duality for this
theory. The index computation provides combinatorial identities for a dual
pair, which we carry out intensive numerical checks.
