Divisibility — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Divisibility — 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
1990 AMC 8 Problem 22 • 1994 AMC 8 Problem 6 • 1994 AMC 8 Problem 10 • 2000 AMC 8 Problem 11 • 2001 AMC 8 Problem 18 • 2001 AMC 8 Problem 25 • 2003 AMC 8 Problem 12 • 2007 AMC 8 Problem 24 • 2008 AMC 8 Problem 15 • 2009 AMC 8 Problem 13 • 2012 AMC 8 Problem 13 • 2013 AMC 8 Problem 1 • 2013 AMC 8 Problem 13 • 2014 AMC 8 Problem 8 • 2014 AMC 8 Problem 21 • 2015 AMC 8 Problem 14 • 2016 AMC 8 Problem 24 • 2017 AMC 8 Problem 8 • 2018 AMC 8 Problem 3 • 2018 AMC 8 Problem 7 • 2019 AMC 8 Problem 13 • 2019 AMC 8 Problem 23 • 2020 AMC 8 Problem 19 • 2024 AMC 8 Problem 5 • 2024 AMC 8 Problem 9 • 2024 AMC 8 Problem 16 • 2025 AMC 8 Problem 6 • 2026 AMC 8 Problem 16 • 2026 AMC 8 Problem 18
AMC 10
2000 AMC 10 Problem 14 • 2001 AMC 10 Problem 12 • 2002 AMC 10B Problem 7 • 2002 AMC 10B Problem 16 • 2003 AMC 10A Problem 24 • 2003 AMC 10A Problem 25 • 2003 AMC 10B Problem 18 • 2003 AMC 10B Problem 25 • 2004 AMC 10B Problem 4 • 2005 AMC 10A Problem 21 • 2005 AMC 10B Problem 22 • 2006 AMC 10B Problem 25 • 2007 AMC 10A Problem 22 • 2007 AMC 10B Problem 24 • 2007 AMC 10B Problem 25 • 2008 AMC 10A Problem 9 • 2009 AMC 10A Problem 1 • 2009 AMC 10A Problem 2 • 2009 AMC 10A Problem 19 • 2010 AMC 10A Problem 4 • 2010 AMC 10B Problem 21 • 2010 AMC 10B Problem 25 • 2011 AMC 10A Problem 2 • 2011 AMC 10A Problem 10 • 2013 AMC 10A Problem 21 • 2014 AMC 10B Problem 14 • 2015 AMC 10B Problem 3 • 2015 AMC 10B Problem 16 • 2017 AMC 10A Problem 16 • 2017 AMC 10A Problem 25 • 2017 AMC 10B Problem 1 • 2017 AMC 10B Problem 25 • 2018 AMC 10A Problem 17 • 2018 AMC 10B Problem 16 • 2018 AMC 10B Problem 19 • 2019 AMC 10A Problem 2 • 2019 AMC 10A Problem 9 • 2019 AMC 10A Problem 25 • 2019 AMC 10B Problem 7 • 2019 AMC 10B Problem 14 • 2020 AMC 10A Problem 6 • 2020 AMC 10A Problem 9 • 2020 AMC 10A Problem 22 • 2020 AMC 10B Problem 7 • 2021 AMC 10A Spring Problem 11 • 2021 AMC 10B Spring Problem 16 • 2021 AMC 10A Fall Problem 5 • 2021 AMC 10A Fall Problem 8 • 2021 AMC 10B Fall Problem 7 • 2022 AMC 10B Problem 17 • 2023 AMC 10A Problem 3 • 2023 AMC 10A Problem 12 • 2024 AMC 10A Problem 5 • 2024 AMC 10A Problem 19 • 2025 AMC 10A Problem 17 • 2025 AMC 10B Problem 8 • 2025 AMC 10B Problem 10 • 2025 AMC 10B Problem 22
AMC 12
1951 AMC 12 Problem 15 • 1951 AMC 12 Problem 19 • 1952 AMC 12 Problem 38 • 1953 AMC 12 Problem 36 • 1954 AMC 12 Problem 49 • 1956 AMC 12 Problem 34 • 1957 AMC 12 Problem 24 • 1957 AMC 12 Problem 32 • 1959 AMC 12 Problem 29 • 1960 AMC 12 Problem 19 • 1960 AMC 12 Problem 25 • 1960 AMC 12 Problem 33 • 1963 AMC 12 Problem 13 • 1964 AMC 12 Problem 16 • 1964 AMC 12 Problem 28 • 1965 AMC 12 Problem 19 • 1966 AMC 12 Problem 26 • 1966 AMC 12 Problem 29 • 1967 AMC 12 Problem 1 • 1967 AMC 12 Problem 15 • 1967 AMC 12 Problem 22 • 1967 AMC 12 Problem 25 • 1967 AMC 12 Problem 30 • 1967 AMC 12 Problem 36 • 1968 AMC 12 Problem 15 • 1968 AMC 12 Problem 19 • 1969 AMC 12 Problem 23 • 1970 AMC 12 Problem 4 • 1970 AMC 12 Problem 31 • 1970 AMC 12 Problem 34 • 1971 AMC 12 Problem 12 • 1971 AMC 12 Problem 14 • 1973 AMC 12 Problem 18 • 1973 AMC 12 Problem 31 • 1975 AMC 12 Problem 16 • 1976 AMC 12 Problem 15 • 1978 AMC 12 Problem 30 • 1979 AMC 12 Problem 22 • 1980 AMC 12 Problem 15 • 1981 AMC 12 Problem 7 • 1981 AMC 12 Problem 11 • 1982 AMC 12 Problem 28 • 1985 AMC 12 Problem 4 • 1985 AMC 12 Problem 12 • 1985 AMC 12 Problem 18 • 1986 AMC 12 Problem 4 • 1987 AMC 12 Problem 3 • 1987 AMC 12 Problem 5 • 1991 AMC 12 Problem 12 • 1991 AMC 12 Problem 17 • 1991 AMC 12 Problem 26 • 1992 AMC 12 Problem 10 • 1992 AMC 12 Problem 13 • 1994 AMC 12 Problem 28 • 1995 AMC 12 Problem 11 • 1997 AMC 12 Problem 20 • 1999 AMC 12 Problem 14 • 2000 AMC 12 Problem 9 • 2001 AMC 12 Problem 21 • 2002 AMC 12B Problem 4 • 2002 AMC 12B Problem 12 • 2002 AMC 12B Problem 21 • 2003 AMC 12A Problem 12 • 2003 AMC 12B Problem 12 • 2004 AMC 12B Problem 22 • 2005 AMC 12A Problem 23 • 2006 AMC 12A Problem 9 • 2006 AMC 12B Problem 19 • 2007 AMC 12A Problem 11 • 2007 AMC 12B Problem 18 • 2007 AMC 12B Problem 24 • 2010 AMC 12A Problem 20 • 2010 AMC 12B Problem 11 • 2010 AMC 12B Problem 21 • 2011 AMC 12A Problem 7 • 2012 AMC 12B Problem 24 • 2013 AMC 12A Problem 17 • 2014 AMC 12B Problem 7 • 2014 AMC 12B Problem 10 • 2015 AMC 12B Problem 3 • 2016 AMC 12B Problem 22 • 2017 AMC 12A Problem 12 • 2017 AMC 12A Problem 21 • 2017 AMC 12B Problem 19 • 2017 AMC 12B Problem 21 • 2017 AMC 12B Problem 25 • 2018 AMC 12A Problem 12 • 2018 AMC 12B Problem 14 • 2018 AMC 12B Problem 15 • 2018 AMC 12B Problem 19 • 2019 AMC 12A Problem 13 • 2019 AMC 12B Problem 5 • 2020 AMC 12A Problem 4 • 2021 AMC 12A Fall Problem 4 • 2021 AMC 12A Fall Problem 12 • 2021 AMC 12B Fall Problem 25 • 2022 AMC 12B Problem 15 • 2023 AMC 12A Problem 3 • 2023 AMC 12A Problem 13 • 2025 AMC 12B Problem 6 • 2025 AMC 12B Problem 23
AIME
1984 AIME Problem 2 • 1986 AIME Problem 5 • 1987 AIME Problem 5 • 1987 AIME Problem 11 • 1989 AIME Problem 3 • 1990 AIME Problem 3 • 1994 AIME Problem 10 • 1994 AIME Problem 12 • 1995 AIME Problem 8 • 1997 AIME Problem 3 • 1997 AIME Problem 6 • 1999 AIME Problem 1 • 2000 AIME I Problem 5 • 2001 AIME I Problem 1 • 2002 AIME I Problem 11 • 2002 AIME II Problem 3 • 2002 AIME II Problem 5 • 2003 AIME II Problem 2 • 2005 AIME II Problem 13 • 2006 AIME I Problem 3 • 2006 AIME II Problem 3 • 2006 AIME II Problem 14 • 2007 AIME II Problem 2 • 2008 AIME I Problem 6 • 2008 AIME II Problem 8 • 2009 AIME II Problem 7 • 2010 AIME II Problem 1 • 2012 AIME I Problem 1 • 2013 AIME I Problem 2 • 2013 AIME I Problem 8 • 2015 AIME I Problem 11 • 2015 AIME II Problem 1 • 2016 AIME I Problem 5 • 2016 AIME I Problem 10 • 2016 AIME II Problem 4 • 2016 AIME II Problem 7 • 2017 AIME I Problem 2 • 2017 AIME II Problem 8 • 2019 AIME II Problem 12 • 2020 AIME I Problem 4 • 2020 AIME I Problem 10 • 2020 AIME II Problem 10 • 2021 AIME I Problem 5 • 2021 AIME II Problem 11 • 2022 AIME II Problem 1 • 2022 AIME II Problem 8 • 2025 AIME I Problem 1 • 2025 AIME I Problem 5 • 2025 AIME II Problem 2 • 2026 AIME II Problem 1 • 2026 AIME II Problem 10