number theory
Greatest common divisor — AMC & AIME Problems
67 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Greatest common divisor — 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: Greatest Common Factor (GCF) — Definition & Examples, Computing GCD and LCM with Prime Factorization, Basic Euclidean Algorithm.
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
- 1954 AMC 12 Problem 4
- 1959 AMC 12 Problem 42
- 1960 AMC 12 Problem 8
- 1968 AMC 12 Problem 15
- 1970 AMC 12 Problem 34
- 1971 AMC 12 Problem 12
- 1972 AMC 12 Problem 34
- 1973 AMC 12 Problem 29
- 1976 AMC 12 Problem 15
- 1985 AMC 12 Problem 26
- 1987 AMC 12 Problem 25
- 1989 AMC 12 Problem 16
- 1990 AMC 12 Problem 19
- 2003 AMC 12B Problem 12
- 2005 AMC 12A Problem 12
- 2006 AMC 12A Problem 14
- 2006 AMC 12B Problem 25
- 2007 AMC 12B Problem 24
- 2010 AMC 12A Problem 20
- 2010 AMC 12B Problem 3
- 2013 AMC 12B Problem 14
- 2016 AMC 12B Problem 24
- 2018 AMC 12B Problem 19
- 2020 AMC 12A Problem 21
- 2021 AMC 12B Fall Problem 16
- 2022 AMC 12A Problem 4
- 2023 AMC 12B Problem 15
- 2023 AMC 12B Problem 24
AIME
- 1985 AIME Problem 13
- 1988 AIME Problem 8
- 1991 AIME Problem 5
- 1992 AIME Problem 5
- 1996 AIME Problem 14
- 2000 AIME I Problem 3
- 2000 AIME I Problem 12
- 2005 AIME II Problem 4
- 2007 AIME II Problem 5
- 2012 AIME I Problem 15
- 2014 AIME I Problem 3
- 2016 AIME I Problem 5
- 2016 AIME I Problem 14
- 2017 AIME I Problem 2
- 2019 AIME I Problem 7
- 2021 AIME I Problem 7
- 2021 AIME I Problem 10
- 2021 AIME II Problem 9
- 2023 AIME II Problem 5
- 2025 AIME II Problem 11
- 2026 AIME II Problem 1
More number theory concepts
- Chicken McNugget Theorem
- Chinese Remainder Theorem
- Continued fraction
- Digits
- Diophantine Equation
- Divisibility
- Euler’s Totient Function
- Factor
- Factor counting
- Fermat’s Little Theorem
- 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