number theory
Factor counting — AMC & AIME Problems
62 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Factor counting — 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Number of Factors of an Integer.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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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
AMC 10
- 2005 AMC 10A Problem 15
- 2009 AMC 10A Problem 19
- 2010 AMC 10B Problem 8
- 2012 AMC 10B Problem 10
- 2013 AMC 10A Problem 19
- 2016 AMC 10A Problem 22
- 2016 AMC 10B Problem 18
- 2017 AMC 10B Problem 20
- 2018 AMC 10B Problem 19
- 2019 AMC 10B Problem 19
- 2020 AMC 10A Problem 15
- 2020 AMC 10A Problem 22
- 2021 AMC 10A Fall Problem 23
- 2021 AMC 10B Fall Problem 6
- 2023 AMC 10A Problem 14
- 2024 AMC 10B Problem 8
AMC 12
- 1964 AMC 12 Problem 28
- 1974 AMC 12 Problem 26
- 2000 AMC 12 Problem 7
- 2003 AMC 12A Problem 8
- 2003 AMC 12A Problem 23
- 2005 AMC 12B Problem 21
- 2008 AMC 12B Problem 23
- 2010 AMC 12B Problem 3
- 2013 AMC 12B Problem 25
- 2016 AMC 12A Problem 18
- 2016 AMC 12B Problem 16
- 2017 AMC 12B Problem 16
- 2018 AMC 12B Problem 14
- 2021 AMC 12A Spring Problem 25
- 2021 AMC 12A Fall Problem 20
- 2022 AMC 12A Problem 25
AIME
- 1986 AIME Problem 8
- 1987 AIME Problem 3
- 1988 AIME Problem 5
- 1990 AIME Problem 5
- 1995 AIME Problem 6
- 1995 AIME Problem 11
- 1996 AIME Problem 8
- 2000 AIME II Problem 2
- 2000 AIME II Problem 4
- 2004 AIME II Problem 8
- 2005 AIME I Problem 2
- 2005 AIME I Problem 3
- 2005 AIME I Problem 12
- 2005 AIME II Problem 4
- 2006 AIME II Problem 13
- 2010 AIME I Problem 1
- 2011 AIME I Problem 7
- 2016 AIME II Problem 11
- 2019 AIME I Problem 9
- 2019 AIME II Problem 3
- 2019 AIME II Problem 9
- 2020 AIME I Problem 12
- 2023 AIME II Problem 10
- 2026 AIME I Problem 6
- 2026 AIME II Problem 9
More number theory concepts
- Chicken McNugget Theorem
- Chinese Remainder Theorem
- Continued fraction
- Digits
- Diophantine Equation
- Divisibility
- Euler’s Totient Function
- Factor
- Fermat’s Little Theorem
- Greatest common divisor
- Least common multiple
- Legendre’s Formula
- Modular arithmetic
- Modular exponentiation
- Multiple
- Multiplicative order
- Palindrome
- Parity
- Perfect power
- Perfect square
- Power of 2
- Prime
- Prime factorization
- Quadratic residue
- Sum of factors
- Trailing zeros
- Triangular number
- Units digit