Number theory Worksheets
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Easy
10 problemsMedium
20 problemsHard
20 problemsMixed
30 problemsFree printable number theory worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from primality, primes in a range at the easy level through to euclidean algorithm, larger diophantine, euclid's prime proof at the advanced level.
What is number theory?
Number theory is the branch of mathematics that studies the properties and relationships of whole numbers, especially positive integers. It explores concepts like prime numbers, divisibility, factors, multiples, and the patterns that emerge when numbers interact through addition, multiplication, and division.
Number theory forms the foundation for understanding fractions, algebra, and modular arithmetic used in cryptography and computer science. Students encounter these ideas when simplifying fractions, finding common denominators, solving equations, and later in coding and digital security systems that protect online information.
Pick a difficulty
Click any level to open the generator with that difficulty pre-selected.
Beginner
Generate →- Concepts
- Primality, primes in a range
- Range
- 2–3 digit numbers
- Steps
- 1–2 steps
- Example
- Is 91 prime? Justify.
Easy
Generate →- Concepts
- Prime factorization (fundamental theorem of arithmetic)
- Range
- up to ~300
- Steps
- 2–4 steps
- Example
- Write 84 as a product of primes.
Medium
Generate →- Concepts
- Linear diophantine equations a·x + b·y = c
- Range
- coefficients 2–30
- Steps
- 3–4 steps
- Example
- Solve 5x + 3y = 11 over the integers.
Hard
Generate →- Concepts
- Euclidean algorithm, larger diophantine, Euclid's prime proof
- Range
- coefficients up to ~250
- Steps
- 4–6 steps
- Example
- Solve 240x + 46y = 8 over the integers.
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