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With a shovel pass to Ty Montgomery that accounted for just 1 yard, Aaron Rodgers became the fastest quarterback in N.F.L. history to record 300 career passing touchdowns. Rodgers accomplished the feat with his 4,741st career pass, easily beating the previous record, which was set when Peyton Manning did it 5,306th attempt. He did it in 13 fewer games than Dan Marino, who was the record-holder when measured that way.