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Starting with a two-body effective nucleon-nucleon interaction, it is shownthat the infinite nuclear matter model of atomic nuclei is more appropriatethan the conventional Bethe-Weizsacker like mass formulae to extract saturationproperties of nuclear matter from nuclear masses. In particular, the saturationdensity thus obtained agrees with that of electron scattering data and theHartree-Fock calculations. For the first time using nuclear mass formula, theradius constant $r_0$=1.138 fm and binding energy per nucleon $a_v$ = -16.11MeV, corresponding to the infinite nuclear matter, are consistently obtainedfrom the same source. An important offshoot of this study is the determinationof nuclear matter incompressibility $K_{\infty}$ to be 288$\pm$ 28 MeV usingthe same source of nuclear masses as input.Comment: 14 latex pages, five figures available on request ( to appear in Phy.  Rev. C

Saturation properties and incompressibility of nuclear matter: A consistent determination from nuclear masses