Number Theory Calculators

20 free number theory calculators in Math.

Chinese Remainder Theorem CalculatorSolve a system of simultaneous congruences with pairwise coprime moduli via CRT.
Common Factor CalculatorList all factors shared by a set of numbers, not just the greatest one.
Composite Number CheckerDetermine whether a number is composite and show its smallest factor.
Divisibility CheckerCheck whether one integer evenly divides another and show the quotient and remainder.
Euclidean Algorithm CalculatorFind the GCD of two numbers with full step-by-step Euclidean algorithm trace.
Euler Totient CalculatorCompute Euler's totient φ(n) — the count of integers up to n that are coprime to n.
Extended Euclidean Algorithm CalculatorFind GCD and Bézout coefficients x, y such that ax + by = gcd(a, b).
Factor CalculatorList every factor of a number and identify whether it's prime.
Factorial CalculatorCompute n! exactly using BigInt for arbitrarily large results up to 1000!.
Fibonacci CalculatorCompute the nth Fibonacci number and display the sequence up to that term.
Greatest Common Factor CalculatorFind the GCF of several numbers using the Euclidean algorithm.
Least Common Multiple CalculatorFind the LCM of several numbers, with the prime factorization behind it.
Lucas Numbers CalculatorCompute the nth Lucas number and display the Lucas sequence up to that term.
Mersenne Prime CheckerTest whether 2ⁿ − 1 is a Mersenne prime for a given exponent n.
Modular Inverse CalculatorFind the modular multiplicative inverse a⁻¹ mod m using the extended Euclidean algorithm.
Perfect Number CheckerDetermine whether a number equals the sum of its proper divisors.
Prime CheckerTest whether a given integer is prime, with trial-division proof.
Prime Factorization CalculatorBreak any number into its prime factors with a factor tree.
Prime Number GeneratorGenerate all prime numbers up to a given limit using the Sieve of Eratosthenes.
Twin Prime CheckerCheck whether two numbers form a twin prime pair (both prime, difference of 2).