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Exciting proposals for a new Higgs factory collider, aimed at the search for new physics and precision studies of particles and forces, especially measurement of the Higgs boson couplings at the loop level, will be evaluated as part of the Snowmass process. Potential facilities include (among others) ILC, FCC-ee, C3, CEPC, CLIC, muon collider and advanced accelerator concepts being investigated by Snowmass topical group AF6, potentially located in Asia, Europe, or the United States. The European Strategy has endorsed an electron-positron Higgs factory as its highest priority after HL-LHC. Much of the detector, software, and physics preparative studies needed for these machines is in common, and is currently being implemented by physicists world-wide. In this white paper for the 2021 Snowmass process we look at current global activity on future Higgs factories and give examples of investments that could be made in these common areas over the next five years to establish a leadership role for the U.S. in a future Higgs factory, wherever it is built. The U.S. high energy physics program confronts a number of challenges that a strong role in the study of the Higgs boson can address. These include, in addition to the scientific results, maintaining leading roles in international partnerships, nurturing and advancing world-leading capabilities and expert resources, and maintaining and attracting talent. The international effort would benefit from increased U.S. participation, and the U.S., in turn, would maintain stature through the partnership.