Tom Brady has the most career passing touchdowns by a quarterback, with 581 touchdowns.

which quarterback has won the most touchdowns
Interpreted as:
Which quarterback has won the most passing touchdowns?
BradyBreesManningFavreRiversMarinoRodgersRoethlisbergerManningRyanTarkentonElwayPalmerMoonUnitasStaffordTestaverdeMontanaWilsonKriegJurgensenFoutsBledsoe581571539508421420412396366347342300294291290282275273267261255254251
NAMEGPTDWCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Tom BradyTom Brady3015812306,77810,59864.079,2047.5263.15.51911.85213,27297.3
Drew BreesDrew Brees2875711727,14210,55167.780,3587.6280.05.42432.34202,99198.7
Peyton ManningPeyton Manning2665391876,1259,38065.371,9407.7270.55.72512.73031,95396.5
Brett FavreBrett Favre3025081886,30010,16962.071,8387.1237.95.03363.35253,48786.0
Philip RiversPhilip Rivers2444211375,2778,13464.963,4407.8260.05.22092.64652,84295.2
Dan MarinoDan Marino2424201474,9678,35859.461,3617.3253.65.02523.02701,93086.4
Aaron RodgersAaron Rodgers1974121294,2856,58765.151,2457.8260.16.3891.44683,150103.9
Ben RoethlisbergerBen Roethlisberger2333961575,0507,83864.460,3487.7259.05.12012.65163,43894.0
Eli ManningEli Manning2363661184,8958,11960.357,0237.0241.64.52443.04112,87084.1
Matt RyanMatt Ryan2053471134,8677,44365.455,7677.5272.04.71582.14102,70694.5
Fran TarkentonFran Tarkenton2463421263,6866,46757.047,0037.3191.15.32664.180.4
John ElwayJohn Elway2343001494,1237,25056.951,4757.1220.04.12263.15163,78579.9
Carson PalmerCarson Palmer182294923,9416,30762.546,2477.3254.14.71873.03402,36487.9
Warren MoonWarren Moon2082911053,9886,82358.449,3257.2237.14.32333.44583,41580.9
Johnny UnitasJohnny Unitas2102901322,8305,18654.640,2397.8191.65.62534.978.2
Matthew StaffordMatthew Stafford165282743,8986,22462.645,1097.2273.44.51442.33852,49689.9
Vinny TestaverdeVinny Testaverde233275983,7876,70156.546,2336.9198.44.12674.04172,99275.0
Joe MontanaJoe Montana1922731273,4095,39163.240,5517.5211.25.11392.692.3
Russell WilsonRussell Wilson144267982,8204,33565.133,9467.8235.76.2811.93942,572101.7
Dave KriegDave Krieg2132611143,1055,31158.538,1477.2179.14.91993.781.5
Sonny JurgensenSonny Jurgensen2182551072,4334,26257.132,2247.6147.86.01894.482.6
Dan FoutsDan Fouts181254883,2975,60458.843,0407.7237.84.52424.380.2
Drew BledsoeDrew Bledsoe194251983,8396,71757.244,6116.6230.03.72063.14673,13577.1
Tony RomoTony Romo156248922,8294,33565.334,1837.9219.15.71172.72481,67297.1
Boomer EsiasonBoomer Esiason187247862,9695,20557.037,9207.3202.84.71843.53182,43881.1
StatMuse has game-level data for passing touchdowns going back to the 1950 season.

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