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We measure the star formation rate (SFR) per unit gas mass and the star formation efficiency (SFE$_{\rm gas}$ for total gas, SFE$_{\rm mol}$ for the molecular gas) in 81 nearby galaxies selected from the EDGE-CALIFA survey, using $^{12}$CO(J=1-0) and optical IFU data. For this analysis we stack CO spectra coherently by using the velocities of H$\alpha$ detections to detect fainter CO emission out to galactocentric radii $r_{\rm gal} \sim 1.2 r_{25}$ ($\sim 3 R_{\rm e}$), and include the effects of metallicity and high surface densities in the CO-to-H$_2$ conversion. We determine the scale lengths for the molecular and stellar components, finding a close to 1:1 relation between them. This result indicates that CO emission and star formation activity are closely related. We examine the radial dependence of SFE$_{\rm gas}$ on physical parameters such as galactocentric radius, stellar surface density $\Sigma_{\star}$, dynamical equilibrium pressure $P_{\rm DE}$, orbital timescale $\tau_{\rm orb}$, and the Toomre $Q$ stability parameter (including star and gas $Q_{\rm star+gas}$). We observe a generally smooth, continuous exponential decline in the SFE$_{\rm gas}$ with $r_{\rm gal}$. The SFE$_{\rm gas}$ dependence on most of the physical quantities appears to be well described by a power-law. Our results also show a flattening in the SFE$_{\rm gas}$-$\tau_{\rm orb}$ relation at $\log[\tau_{\rm orb}]\sim 7.9-8.1$ and a morphological dependence of the SFE$_{\rm gas}$ per orbital time, which may reflect star formation quenching due to the presence of a bulge component. We do not find a clear correlation between SFE$_{\rm gas}$ and $Q_{\rm star+gas}$., Comment: 24 pages, 12 figures, 1 Table