At least 20 times, a team has held all opponents scoreless for an entire season.
Where there has been a name change, this list gives the current name of the institution:
Auburn University (1914)
University of Michigan (1885, 1886, 1887, 1901)
Penn State (1887)
Yale (1888, 1909)
North Dakota State (1902)
Saint Louis University (1904)
Washington state (1906)
Oregon State (1907)
University of Pittsburgh (1910)
Texas A&M (1917, 1919)
Colgate University (1932)
Grambling State (1942)
Eastern Michigan University (1943)
The fewest points allowed by a school that did not finish the season undefeated was 7. This happened twice. In both cases, the school have gave up a single touchdown in their season-ending bowl game and lost 7-0: Appalachian State (1937 to Southern Mississippi) and Duke University (1938 to Southern California in the Rose Bowl). In 1939, Tennessee accomplished this during the regular season as well, and lost their bowl game 14-0; ironically, Tennessee was also defeated in the Rose Bowl by Southern California.
That would be Tennessee in 1939......Zero The next best in the modern era I believe is the 2001 Miami Hurricanes......9.75... take that and include the Offense scoring an average of 42.6 per game and you have a good case for one heck of a football team, some consider the 'best'.
Bevo Francis, #32 for Rio Grande College, scored 113 pts in an NCAA Division II games against Hillsdale College.
The average total points scored in final division 1 NCAA men's basketball is between 128 and 145. This is the combined score of both teams.
Wyoming scored 103
John Pierce of David Lipscomb College: 4230 points. According to the NCAA record book, David Lipscomb College was not a recognized NCAA school when Hutcheson and Pierce played. I believe Lipscomb is now an NCAA recognized division 3 school. The all-time NCAA-recognized points leader is Travis Grant of Kentucky State (div 2) with 4045 points.
3 to 5 SC vs Maryland I think
as I tallied it, with the play-in game counted, the total points scored came to 8728
UNLV scored 103 points against Duke's 73 in the 1990 NCAA Men's Basketball Championship game.