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I don't know exactly how many schools have won both hoops and football at ANY time, but here's at least a partial list that's pretty close. I've included only AP football champs, which started in 1936:
Florida
Michigan
Ohio State
Syracuse
Maryland
Michigan State
Stanford, Arkansas, and UCLA won seemingly legitimate non-AP national championships that were recognized in football at the time (e.g. UPI), and have, of course, won the hoops title outright. There are a few others like Wisconsin that appear to have won what I call "historical" championships in football based either on regressed computer polls or something similar.
If you go back farther than the 30's and recognize other national champs (in football), you have Cal.
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