number theory
Factor — AMC & AIME Problems
43 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Factor — 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: What Are Factors? — Definition & Examples, Finding Factors of a Number — Theory & Examples.
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
AMC 10
AMC 12
- 1960 AMC 12 Problem 31
- 1961 AMC 12 Problem 33
- 1962 AMC 12 Problem 38
- 1973 AMC 12 Problem 21
- 1975 AMC 12 Problem 22
- 1984 AMC 12 Problem 21
- 2002 AMC 12A Problem 20
- 2008 AMC 12B Problem 16
- 2011 AMC 12B Problem 15
- 2013 AMC 12A Problem 10
- 2014 AMC 12B Problem 7
- 2019 AMC 12B Problem 14
- 2020 AMC 12B Problem 24
- 2022 AMC 12B Problem 4
- 2023 AMC 12B Problem 14
- 2024 AMC 12A Problem 6
- 2024 AMC 12A Problem 12
More number theory concepts
- Chicken McNugget Theorem
- Chinese Remainder Theorem
- Continued fraction
- Digits
- Diophantine Equation
- Divisibility
- Euler’s Totient Function
- Factor counting
- 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