The Green Bay Packers have the most games by a team with 3+ passing touchdowns, with 237 games.

which nfl about has the most 3 td passing games
Interpreted as:
Which NFL about has the most 3 or more td passing regular-season games?
PackersColtsPatriots49ersEaglesGiantsRamsRedskinsCowboysRaidersLionsChargersVikingsChiefsBearsSteelersSaintsBroncosCardinalsDolphinsBengalsBrownsTitans237193188184184177174170168166165162155148147146145142135133128128119
TEAMGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Green Bay PackersGreen Bay Packers2378074,9577,74564.07.910.42012.63882,655112.4
Indianapolis ColtsIndianapolis Colts1936594,0606,37663.755,5848.7288.010.31802.82802,138114.2
New England PatriotsNew England Patriots1886324,1166,47263.654,9518.5292.39.81432.23112,156113.8
San Francisco 49ersSan Francisco 49ers1846073,8556,00064.352,7828.8286.910.11702.83082,003114.2
Philadelphia EaglesPhiladelphia Eagles1846153,5975,92660.78.210.41873.2108.3
New York GiantsNew York Giants1776033,2985,48260.28.011.01813.3108.6
Los Angeles RamsLos Angeles Rams1745943,4555,53862.48.110.71843.3109.7
Washington RedskinsWashington Redskins1705693,3065,36961.67.410.61843.4105.2
Dallas CowboysDallas Cowboys1685553,3995,30964.048,2039.1286.910.51472.83202,320116.6
Las Vegas RaidersLas Vegas Raiders1665583,2255,34060.445,0918.4271.610.41492.83142,320110.8
Detroit LionsDetroit Lions1655383,2905,47760.17.79.82033.7101.4
Los Angeles ChargersLos Angeles Chargers1625393,5335,52763.948,7678.8301.09.81773.22511,747111.3
Minnesota VikingsMinnesota Vikings1555253,3345,28263.145,1048.5291.09.91222.33382,369113.8
Kansas City ChiefsKansas City Chiefs1484952,8854,60662.641,4159.0279.810.71182.62511,797116.9
Chicago BearsChicago Bears1474892,8014,66360.16.710.51914.197.8
Pittsburgh SteelersPittsburgh Steelers1464922,9774,72763.041,3128.7283.010.41473.13022,221112.7
New Orleans SaintsNew Orleans Saints1454913,5705,28767.545,0578.5310.79.31182.22461,694115.5
Denver BroncosDenver Broncos1424793,1134,96862.741,1338.3289.79.61523.12511,960108.2
Arizona CardinalsArizona Cardinals1354462,6984,53159.58.19.81773.9102.2
Miami DolphinsMiami Dolphins1334472,8624,60562.138,3678.3288.59.71453.11951,506107.8
Cincinnati BengalsCincinnati Bengals1284202,7144,19764.736,1618.6282.510.0922.22461,740116.1
Cleveland BrownsCleveland Browns1284332,4093,95960.834,7168.8271.210.91543.92271,752109.6
Tennessee TitansTennessee Titans1194062,3754,01759.133,5508.4281.910.11433.61911,424105.0
Atlanta FalconsAtlanta Falcons1183842,5383,98263.733,6908.5285.59.6792.02321,599114.3
New York JetsNew York Jets1184002,3603,96059.632,5748.2276.110.11323.32131,676105.8
Buffalo BillsBuffalo Bills1163892,2413,61861.931,8058.8274.210.81042.92081,507114.2
Seattle SeahawksSeattle Seahawks1053632,2283,37266.129,5828.8281.710.8832.52301,577119.3
Tampa Bay BuccaneersTampa Bay Buccaneers772661,7722,78963.523,6568.5307.29.5853.0112712109.5
Baltimore RavensBaltimore Ravens551831,1961,85264.615,1048.2274.69.9492.6103667111.8
Carolina PanthersCarolina Panthers551801,1461,83562.515,1638.3275.79.8412.2106737111.9
Jacksonville JaguarsJacksonville Jaguars421379011,42463.311,3828.0271.09.6241.789551113.2
Houston TexansHouston Texans401409951,49266.712,7788.6319.59.4291.988565116.5
StatMuse has team, game-level data for passing touchdowns going back to the 1940 season.

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