Free Number Theory Calculators

GCD & LCM Calculator — Up to 10 Numbers

Find the GCD and LCM of up to 10 integers using the Euclidean algorithm. Shows prime factorization, divisibility check, and full step-by-step working.

Prime Factorization Calculator

Find the prime factorization of any positive integer and check primality.

Factorial Calculator — n!, n!! & Derangements

Calculate standard factorial (n!), double factorial (n!!), and subfactorial (!n / derangements) with exact BigInt arithmetic, scientific notation, digit count, trailing zeros, Stirling approximation, and step-by-step working.

Fibonacci Calculator — F(n), Sequence & Check

Find any Fibonacci number F(n) with exact BigInt arithmetic up to F(10000), generate sequences with golden ratio convergence, and check whether any integer is a Fibonacci number using the algebraic 5n²±4 perfect-square test.

Prime Number Checker

Check if any number is prime using an optimized trial division algorithm. Also lists factors.

Perfect Number Checker

Check if a number is perfect, abundant, or deficient and find all its proper divisors.

Roman Numeral Converter

Convert between Arabic numbers and Roman numerals (I, V, X, L, C, D, M).

Number Sequence Calculator

Find the nth term of arithmetic, geometric, and other common sequences.

Digital Root Calculator

Calculate the digital root (iterated sum of digits), additive persistence, Harshad check, and multiplicative digital root for any integer up to 300 digits.