Your source is not very accurate. Harding was sworn in as President in March 1921 and died in August 1923, so he was in office 2 years and almost 5 months. Some members of his administration were involved in scandals (most famously the Teapot Dome scandal) but Harding doesn't seem have been personally involved in any corruption. (Being faithful to his wife was another matter.)
Although he made some bad choices in picking men for his administration, he also had some excellent Cabinet officers. He was the first President to go to the South and speak out against racial segregation.