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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).
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
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
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