In the Kerr rotation geometry, magneto optic memory devices typically suffer from low figure-of-merit (FOM) and long write times. We show that skyrmions formed at the interface of a thin-film multiferroic and a topological insulator can give rise to high FOM magneto optic Kerr effects (MOKEs). Huge differential MOKE can arise in parts of the phase diagram. Resonance like features in the MOKE spectra arising from the induced low energy TI bandgap, the multiferroic-film thickness, and the high energy Drude like behavior are resolved and explained. The Fermi level dependence of the MOKE signatures is distinct for the different magnetic textures. This has broad implications for magnetic texture characterization, electro-optic modulators and isolators and high density magnetic optic memory. PACS numbers: Magneto-optic (MO) phenomenon such as Kerr and Faraday rotations, Voigt effect, magneto-plasma reflections and cyclotron resonances arise from broken time reversal symmetry. Some MO effects also arise from the electronic structure's topology, and hence are used to study quantum hall effects[1], Kerr rotations in topological insulators (TIs)[2, 3], magnetoelectric optical effects[4, 5], magneto-chiral effects[6], and skyrmions and their Hall effects[7-9].arXiv:1805.02799v1 [cond-mat.mes-hall]