Number Theory calculators
These tools explore the properties of whole numbers: primality and prime factorization, GCD and LCM, modular arithmetic and the Chinese remainder theorem, Euler's totient, famous sequences such as Fibonacci, Catalan and Collatz, factorials, continued fractions, Roman numerals and arbitrary-precision arithmetic.
16 tools · Updated October 21, 2026
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Primes, factors and divisors
Every whole number greater than 1 is either prime or a product of primes in exactly one way, apart from order. This is the fundamental theorem of arithmetic, and it is why prime factorization is so useful: once you know the factors, the GCD, the LCM and the number of divisors follow directly. The Prime Factorization Calculator shows the factor tree, and the GCD and LCM Calculator works with up to ten numbers.
For a single yes or no answer, the Prime Number Checker is faster. Euler's totient φ(n) counts the numbers below n that share no factor with it, and the Perfect Number Checker tests whether a number equals the sum of its proper divisors, as 6 = 1 + 2 + 3 does.
Modular arithmetic and cryptography
Modular arithmetic works with remainders, like hours on a clock. It underpins check digits, hash functions and public-key cryptography. The Modular Arithmetic Calculator computes modular inverses and fast modular powers, which are the core operations of RSA.
The Chinese remainder theorem says that if the moduli are pairwise coprime, a set of congruences has exactly one solution modulo their product. Use the Chinese Remainder Theorem Calculator for scheduling and puzzle problems of the form 'leaves remainder 2 when divided by 3 and remainder 3 when divided by 5'.
Sequences, big numbers and representations
Integer sequences appear throughout mathematics: Fibonacci numbers in growth patterns, Catalan numbers in counting bracket arrangements and tree shapes, and the Collatz sequence in a famous unsolved problem. Factorials grow faster than any exponential and reach 3,628,800 at 10!, which is why the Big Number Calculator is useful once results exceed the roughly 15 to 17 significant digits of ordinary floating-point arithmetic.
Continued fractions give the best rational approximations to a number, such as 355/113 for π. The Roman Numeral Converter and Digital Root Calculator handle two older representations that still turn up in dates, clocks and divisibility checks.