Lamar Jackson and Michael Vick are tied for the most games by a quarterback with 100+ rushing yards, with 10 games.

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which quarterback has the most 100 rushing games
Interpreted as:
Which quarterback has the most 100 or more rushing regular-season games?
JacksonVickWilsonNewtonMcNabbCunninghamDouglassKilmerAllenKaepernickPryorFieldsHurtsMurrayHoganManzielMariotaGriffinWebbTebowBrooksStewartYoung1010433333222111111111111
NAMEGPRUSH YDSATTYPCRUSH YDS/GRUSH TDREC YDSRECTRGAVGREC YDS/GREC TD
Lamar JacksonLamar Jackson101,1701637.2117.080000.00
Michael VickMichael Vick101,26912110.5126.950000.00
Russell WilsonRussell Wilson4437459.7109.330000.00
Cam NewtonCam Newton3323349.5107.720000.00
Donovan McNabbDonovan McNabb33323110.7110.730010.00
Randall CunninghamRandall Cunningham33553410.4118.33000.00
Bobby DouglassBobby Douglass3344447.8114.75000.00
Billy KilmerBilly Kilmer3349556.3116.38000.00
Josh AllenJosh Allen22361813.1118.010010.00
Colin KaepernickColin Kaepernick22641715.5132.010000.00
Terrelle PryorTerrelle Pryor2218229.9109.010000.00
Justin FieldsJustin Fields11031010.3103.010000.00
Jalen HurtsJalen Hurts1106185.9106.000000.00
Kyler MurrayKyler Murray1106119.6106.010000.00
Kevin HoganKevin Hogan1104714.9104.010000.00
Johnny ManzielJohnny Manziel1108119.8108.000000.00
Marcus MariotaMarcus Mariota1112912.4112.010000.00
Robert Griffin IIIRobert Griffin III11381310.6138.020000.00
Joe WebbJoe Webb1109715.6109.010000.00
Tim TebowTim Tebow1118139.1118.000000.00
Aaron BrooksAaron Brooks1108119.8108.000000.00
Kordell StewartKordell Stewart1103714.7103.00000.00
Steve YoungSteve Young1102812.8102.00000.00
Vinny TestaverdeVinny Testaverde1105715.0105.01000.00
Steve GroganSteve Grogan1103714.7103.01000.00
StatMuse has game-level data for rushing yards going back to the 1960 season.