Number Theory

These tools explore the properties of integers. They test primality for numbers up to 1,000 digits, factorise and list divisors with their count and sum, generate primes over a range with the sieve of Eratosthenes, and find the greatest common divisor and least common multiple — plus modular arithmetic, the Chinese remainder theorem for systems of congruences, and Euler’s totient function.

Prime Number Checker – Up to 1,000 Digits, Free

Check if a number up to 1,000 digits is prime — instantly and free. See the factorization, nearest primes, trial-division steps and which test proved it.

Sieve of Eratosthenes Generator (Free) – List Primes & Find the Nth Prime

Enter an upper bound to generate a list of primes with the Sieve of Eratosthenes, visualized step by step. Also look up the Nth prime (up to the 1,000,000th) — free, browser-based, no sign-up.

Prime Factorization Calculator — Free Online Tool (up to 1,000,000)

Free online tool to instantly factorize any integer N from 2 to 1,000,000 into prime factors. Shows step-by-step division, divisors, divisor count, and divisor sum. Includes a 1–100 reference table.

GCD & LCM Calculator

Enter two positive integers to find their greatest common divisor (GCD) using the Euclidean algorithm, with each step of the calculation shown. The least common multiple (LCM) is calculated at the same time.

Modular Arithmetic Calculator (Mod Calculator)

A modular arithmetic calculator with 4 modes: basic mod, modular addition/subtraction/multiplication, modular exponentiation (repeated squaring), and modular inverse (extended Euclidean algorithm). Handles negative mod a...

Chinese Remainder Theorem (CRT) Calculator — Solve Simultaneous Congruences

Solve a system of simultaneous congruences x ≡ a₁ (mod n₁), x ≡ a₂ (mod n₂)... with the Chinese Remainder Theorem. Automatically checks that the moduli are pairwise coprime and returns the smallest non-negative solution...

Euler's Totient Function (φ) Calculator — Coprime Counter

Enter an integer N (1 to 1,000,000) to instantly find the number of integers from 1 to N that are coprime to N (Euler's totient function φ(N)), shown with the full prime factorization and formula, not just the answer. In...