We use color gradients to explore the evolution of early-type galaxies in the core of the massive galaxy cluster MACS J1206.2-0847 at z = 0.44. We used data from the CLASH and CLASH-VLT surveys to perform multiwavelength optimized model fitting using Galapagos-2 from the MegaMorph project to measure their photometric parameters. We derive color gradients for $g_{475} - I_{814}$, $r_{625} - Y_{105}$, $I_{814} - H_{160}$ , and $Y_{105} - H_{160}$ at radii ranging between 0.1 - 2 $r_e$ for 79 early-type cluster galaxies. From synthetic spectral models that use simple star formation recipes, we inferred ages and metallicities of the stellar population at different locations within each galaxy and characterized their influence on the radial color trends. We measure that galaxy sizes are $sim$ 25% smaller in the red $H_{160}$ filter than in the blue $r_{625}$ filter but maintain a constant (within 3$sigma$) S{e}rsic index $n$ with wavelength. We find negative color gradients in all colors with slopes ranging between -0.07 and -0.17 mag dex$^{-1}$ and with no obvious dependence on total magnitude, stellar mass, or location inside the cluster core. We explain the observed radial trends of color gradients as a result of the ages and metallicities of the respective stellar populations. Red galaxy cores are typically $sim$ 3 Gyr older and more enriched in metals than the galaxy outskirts, which are of solar metallicity.
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