Comprehensive collection of free online number theory calculators for students, mathematicians, and developers.
Explore prime numbers, factorization, divisibility, modular arithmetic, and other number properties instantly.
Enter any positive whole number (up to 1,000,000)
Enter a number above to check if it's prime
Our number theory calculators provide instant solutions for various mathematical problems. Follow these simple steps:
Select the specific number theory calculator you need from the dropdown menu
Enter the required numerical values in the input fields
Click calculate or press enter to see the results
Review the detailed mathematical solution displayed
Use the results for your studies, projects, or mathematical research
Check if a number is prime. Try entering 17, 23, or 97 to see they're prime, or 15, 21 to see they're composite.
Find prime factors of a number. Enter 60 to get 2² × 3 × 5, or 100 to get 2² × 5².
Verify if one number divides another evenly. Check if 144 is divisible by 12 (yes), or if 99 is divisible by 7 (no).
Calculate the least common multiple. Find LCM(12, 18) to get 36, or LCM(7, 11) to get 77.
Learn and practice number theory concepts, verify homework solutions, and explore mathematical properties
Analyze prime numbers, modular inverses, and number properties essential for cryptographic algorithms
Solve algorithmic problems involving primes, factors, and number-theoretic functions
Investigate number patterns, verify conjectures, and perform exploratory number theory research
Number theory is a branch of pure mathematics devoted primarily to the study of integers and integer-valued functions. It explores fundamental properties of whole numbers and their relationships, forming the basis for much of modern cryptography and computer science.
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Prime factorization is the decomposition of a composite number into a product of prime numbers, unique up to the order of factors according to the fundamental theorem of arithmetic.
The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers. Modular arithmetic involves performing operations in a number system where numbers 'wrap around' upon reaching a certain value, called the modulus. The modular inverse of a number 'a' modulo 'm' is a number 'x' such that (a × x) ≡ 1 (mod m), if such x exists.
Confusing prime numbers with irreducible polynomials or composite numbers
Remember that 1 is not considered prime, and all primes greater than 2 are odd (except 2 itself)
Incorrectly assuming that LCM(a,b) equals a×b without checking for common factors
Use the relationship LCM(a,b) = (a×b) / GCD(a,b) for accurate calculations
Forgetting that modular inverse doesn't exist when the number and modulus share common factors
A modular inverse exists only when the number and modulus are coprime (their GCD is 1)
Using inefficient algorithms for primality testing of large numbers
Our calculator uses optimized methods to determine primality quickly and accurately
Yes, all our number theory calculators are completely free to use with no hidden charges or registration requirements. Simply visit the tool, enter your values, and get instant results.
Our calculators use precise mathematical algorithms and proven theorems to ensure maximum accuracy. Results are computed using exact arithmetic where possible and follow standard mathematical conventions.
No, our number theory calculators run entirely in your web browser. There's no need to download, install, or configure any software. Just access them online from any device with internet connection.
Absolutely! All our number theory tools are designed with responsive layouts that work seamlessly on smartphones, tablets, and desktop computers.
Our collection includes calculators for prime numbers, prime factorization, divisibility testing, LCM computation, modular inverses, and various other number-theoretic functions and properties.
Yes, all calculations happen locally in your browser. We don't store, collect, or transmit your input data to any external servers, ensuring complete privacy and security.
Our calculators support reasonably large integers, though extremely large numbers may be subject to browser JavaScript limitations. For most practical number theory applications, our tools will work effectively.