AMC number theory problems
Divisibility and primes, modular arithmetic, digits and number bases, and Diophantine equations. 553 problems across 26 concepts. 305 come from the AMC 10 and 248 from the AMC 12.
Picks a problem you have not seen, at about the difficulty you are handling.
Concepts in number theory
- Divisibility102
- Digits99
- Modular arithmetic96
- Prime factorization92
- Parity66
- Diophantine Equation58
- Perfect square39
- Prime35
- Factor counting30
- Least common multiple29
- Greatest common divisor28
- Factor21
- Triangular number19
- Units digit14
- Multiple10
- Palindrome10
- Chinese Remainder Theorem9
- Power of 29
- Modular exponentiation7
- Sum of factors7
- Legendre's Formula6
- Continued fraction5
- Perfect power5
- Trailing zeros5
- Multiplicative order4
- Euler's Totient Function3
60 most recent problems
Newest contests first. Every problem opens with its answer choices, hints and a worked solution.
- 2025 AMC 10A · Problem 5
- 2025 AMC 10A · Problem 11
- 2025 AMC 10A · Problem 17
- 2025 AMC 10A · Problem 19
- 2025 AMC 10B · Problem 2
- 2025 AMC 10B · Problem 4
- 2025 AMC 10B · Problem 8
- 2025 AMC 10B · Problem 9
- 2025 AMC 10B · Problem 10
- 2025 AMC 10B · Problem 22
- 2025 AMC 10B · Problem 23
- 2025 AMC 10B · Problem 25
- 2025 AMC 12B · Problem 2
- 2025 AMC 12B · Problem 5
- 2025 AMC 12B · Problem 6
- 2025 AMC 12B · Problem 9
- 2025 AMC 12B · Problem 19
- 2025 AMC 12B · Problem 23
- 2024 AMC 10A · Problem 3
- 2024 AMC 10A · Problem 5
- 2024 AMC 10A · Problem 7
- 2024 AMC 10A · Problem 10
- 2024 AMC 10A · Problem 11
- 2024 AMC 10A · Problem 15
- 2024 AMC 10A · Problem 18
- 2024 AMC 10A · Problem 19
- 2024 AMC 10A · Problem 23
- 2024 AMC 10B · Problem 4
- 2024 AMC 10B · Problem 6
- 2024 AMC 10B · Problem 7
- 2024 AMC 10B · Problem 8
- 2024 AMC 10B · Problem 13
- 2024 AMC 10B · Problem 16
- 2024 AMC 10B · Problem 18
- 2024 AMC 10B · Problem 22
- 2024 AMC 10B · Problem 24
- 2024 AMC 10B · Problem 25
- 2024 AMC 12A · Problem 4
- 2024 AMC 12A · Problem 6
- 2024 AMC 12A · Problem 9
- 2024 AMC 12A · Problem 11
- 2024 AMC 12A · Problem 12
- 2024 AMC 12B · Problem 4
- 2024 AMC 12B · Problem 14
- 2024 AMC 12B · Problem 16
- 2024 AMC 12B · Problem 22
- 2023 AMC 10A · Problem 3
- 2023 AMC 10A · Problem 5
- 2023 AMC 10A · Problem 9
- 2023 AMC 10A · Problem 12
- 2023 AMC 10A · Problem 14
- 2023 AMC 10A · Problem 23
- 2023 AMC 10B · Problem 6
- 2023 AMC 10B · Problem 8
- 2023 AMC 10B · Problem 9
- 2023 AMC 10B · Problem 11
- 2023 AMC 10B · Problem 12
- 2023 AMC 10B · Problem 14
- 2023 AMC 10B · Problem 15
- 2023 AMC 10B · Problem 16
Use Start number theory practice above to work through the remaining 493.