Number Theory on the AMC 10
233 of the 1,300 problems since 2000 (17.9%) have their main idea in this category, spread across 8 topics.
Where it appears on the paper
86
P1-10
47
P11-15
41
P16-20
59
P21-25
By era
72
2000–2009
88
2010–2019
73
2020–2025
Topics in Number Theory
- Bases & Digits43
Non-decimal bases, digit manipulation, digit sums, palindromes
- Diophantine Equations27
Integer solutions of equations, bounding, factoring integer equations
- Divisibility & Factors52
Divisors, number/sum of divisors, factorization, divisibility rules
- Fractions & Decimals14
Repeating decimals, unit fractions, rational number properties, terminating decimals
- GCD & LCM10
GCD/LCM computation, Euclidean algorithm, gcd*lcm = product
- Modular Arithmetic38
Remainders, congruences, last digits, cyclicity, Chinese-remainder style reasoning
- Number Properties32
Perfect squares/cubes, parity, consecutive integers, floor/ceiling, integer sequences
- Primes17
Prime properties, prime factorization, counting with primes