We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that $AdS_ntimes_w M^{10-n}$ preserve $2^{[{nover2}]} k$ for $nleq 4$ and $2^{[{nov
er2}]+1} k$ for $4<nleq 7$ supersymmetries, $kin bN_{>0}$. In addition we show that, for suitably restricted fields and $M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on $M^{10-n}$. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to $bR^{1,n-1}times_w M^{10-n}$ backgrounds which underpin flux compactifications to $bR^{1,n-1}$ and show that these preserve $2^{[{nover2}]} k$ for $2<nleq 4$, $2^{[{n+1over2}]} k$ for $4<nleq 8$, and $2^{[{nover2}]} k$ for $n=9, 10$ supersymmetries.
