Prime factorization — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Prime factorization — a number theory concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
1991 AMC 8 Problem 13 • 1993 AMC 8 Problem 3 • 1995 AMC 8 Problem 22 • 1997 AMC 8 Problem 11 • 2007 AMC 8 Problem 3 • 2009 AMC 8 Problem 11 • 2009 AMC 8 Problem 17 • 2010 AMC 8 Problem 14 • 2011 AMC 8 Problem 17 • 2012 AMC 8 Problem 18 • 2013 AMC 8 Problem 10 • 2016 AMC 8 Problem 9 • 2017 AMC 8 Problem 7 • 2018 AMC 8 Problem 18 • 2020 AMC 8 Problem 17 • 2023 AMC 8 Problem 22
AMC 10
2000 AMC 10 Problem 1 • 2001 AMC 10 Problem 8 • 2001 AMC 10 Problem 12 • 2001 AMC 10 Problem 14 • 2003 AMC 10B Problem 14 • 2004 AMC 10B Problem 4 • 2005 AMC 10A Problem 15 • 2006 AMC 10B Problem 22 • 2007 AMC 10A Problem 17 • 2009 AMC 10A Problem 9 • 2009 AMC 10A Problem 13 • 2009 AMC 10A Problem 25 • 2009 AMC 10B Problem 6 • 2010 AMC 10A Problem 21 • 2011 AMC 10A Problem 10 • 2011 AMC 10B Problem 5 • 2012 AMC 10B Problem 10 • 2013 AMC 10A Problem 21 • 2013 AMC 10A Problem 23 • 2013 AMC 10B Problem 9 • 2013 AMC 10B Problem 20 • 2014 AMC 10A Problem 8 • 2014 AMC 10B Problem 12 • 2016 AMC 10A Problem 22 • 2016 AMC 10A Problem 25 • 2017 AMC 10B Problem 20 • 2018 AMC 10A Problem 7 • 2018 AMC 10A Problem 22 • 2018 AMC 10B Problem 21 • 2019 AMC 10A Problem 11 • 2019 AMC 10B Problem 19 • 2020 AMC 10B Problem 25 • 2021 AMC 10A Spring Problem 18 • 2021 AMC 10B Spring Problem 12 • 2021 AMC 10B Fall Problem 6 • 2021 AMC 10B Fall Problem 8 • 2022 AMC 10A Problem 7 • 2022 AMC 10A Problem 19 • 2023 AMC 10A Problem 5 • 2023 AMC 10B Problem 15 • 2023 AMC 10B Problem 23 • 2024 AMC 10A Problem 5 • 2024 AMC 10B Problem 13 • 2024 AMC 10B Problem 22
AMC 12
1951 AMC 12 Problem 45 • 1954 AMC 12 Problem 4 • 1959 AMC 12 Problem 42 • 1960 AMC 12 Problem 33 • 1963 AMC 12 Problem 8 • 1965 AMC 12 Problem 33 • 1970 AMC 12 Problem 23 • 1974 AMC 12 Problem 26 • 1984 AMC 12 Problem 3 • 1985 AMC 12 Problem 12 • 1986 AMC 12 Problem 23 • 1991 AMC 12 Problem 14 • 1991 AMC 12 Problem 17 • 1993 AMC 12 Problem 15 • 1995 AMC 12 Problem 24 • 1995 AMC 12 Problem 29 • 1996 AMC 12 Problem 29 • 1997 AMC 12 Problem 21 • 2000 AMC 12 Problem 1 • 2000 AMC 12 Problem 23 • 2001 AMC 12 Problem 7 • 2003 AMC 12A Problem 23 • 2003 AMC 12B Problem 18 • 2004 AMC 12B Problem 3 • 2005 AMC 12A Problem 8 • 2005 AMC 12B Problem 17 • 2005 AMC 12B Problem 21 • 2006 AMC 12B Problem 14 • 2009 AMC 12A Problem 18 • 2009 AMC 12B Problem 5 • 2009 AMC 12B Problem 22 • 2010 AMC 12B Problem 9 • 2010 AMC 12B Problem 25 • 2011 AMC 12A Problem 7 • 2011 AMC 12B Problem 4 • 2011 AMC 12B Problem 15 • 2012 AMC 12B Problem 24 • 2013 AMC 12A Problem 17 • 2013 AMC 12A Problem 19 • 2013 AMC 12B Problem 9 • 2013 AMC 12B Problem 15 • 2014 AMC 12B Problem 15 • 2015 AMC 12A Problem 15 • 2015 AMC 12B Problem 18 • 2016 AMC 12A Problem 18 • 2016 AMC 12A Problem 22 • 2016 AMC 12B Problem 24 • 2017 AMC 12B Problem 16 • 2018 AMC 12A Problem 7 • 2018 AMC 12A Problem 19 • 2018 AMC 12B Problem 19 • 2019 AMC 12B Problem 14 • 2020 AMC 12A Problem 21 • 2021 AMC 12A Spring Problem 18 • 2021 AMC 12A Spring Problem 25 • 2021 AMC 12B Spring Problem 7 • 2021 AMC 12A Fall Problem 8 • 2021 AMC 12B Fall Problem 6 • 2021 AMC 12B Fall Problem 12 • 2022 AMC 12A Problem 4 • 2022 AMC 12A Problem 23 • 2023 AMC 12A Problem 4 • 2023 AMC 12A Problem 22 • 2023 AMC 12B Problem 23 • 2023 AMC 12B Problem 24 • 2024 AMC 12A Problem 4
AIME
1983 AIME Problem 8 • 1986 AIME Problem 8 • 1987 AIME Problem 3 • 1987 AIME Problem 7 • 1988 AIME Problem 5 • 1989 AIME Problem 4 • 1990 AIME Problem 5 • 1991 AIME Problem 5 • 1994 AIME Problem 5 • 1995 AIME Problem 6 • 1996 AIME Problem 8 • 1998 AIME Problem 1 • 1999 AIME Problem 7 • 2000 AIME I Problem 1 • 2000 AIME I Problem 11 • 2000 AIME II Problem 4 • 2002 AIME II Problem 5 • 2004 AIME II Problem 3 • 2004 AIME II Problem 8 • 2006 AIME II Problem 3 • 2007 AIME I Problem 1 • 2009 AIME I Problem 13 • 2010 AIME II Problem 3 • 2010 AIME II Problem 10 • 2014 AIME I Problem 6 • 2016 AIME I Problem 12 • 2016 AIME II Problem 8 • 2019 AIME I Problem 7 • 2019 AIME II Problem 3 • 2019 AIME II Problem 9 • 2020 AIME I Problem 7 • 2020 AIME I Problem 9 • 2020 AIME I Problem 10 • 2020 AIME I Problem 12 • 2020 AIME II Problem 1 • 2023 AIME I Problem 4 • 2025 AIME I Problem 10 • 2026 AIME I Problem 8 • 2026 AIME II Problem 13