number theory Calculators
Last updated: May 2026
GCD Calculator
Find the greatest common divisor — the largest integer that divides two whole numbers exactly with no remainder.
LCM Calculator
Find the least common multiple — the smallest positive integer that two numbers both divide into evenly.
Prime Number Checker
Instantly determine whether any positive integer is a prime number.
Factorial Calculator
Compute the factorial n!, the product of all positive integers up to n.
Fibonacci Calculator
Find the exact Fibonacci number at any position in the sequence, where each term is the sum of the two before it.
Modular Arithmetic Calculator
Compute modular addition, subtraction, and multiplication instantly.
Perfect Number Checker
Instantly check whether any positive integer is a perfect number — one that equals the sum of its proper divisors.
Euler's Totient Function
Calculate Euler's totient φ(n) — the count of integers from 1 to n that share no common factor with n.
Divisor Count Calculator
Count exactly how many divisors a positive integer has, including 1 and itself.
Binary to Decimal Converter
Convert any binary (base-2) number to its decimal (base-10) equivalent in one click.
Prime Factorization Calculator
Break any integer into its prime building blocks instantly.
GCD and LCM Calculator
Instantly compute the Greatest Common Divisor and Least Common Multiple of two integers.
Fibonacci Sequence Calculator
Calculate any Fibonacci number by position or generate the full sequence up to a given term.
Perfect Number Calculator
Determine whether any integer is perfect, abundant, or deficient based on its proper divisor sum.
Collatz Conjecture Calculator
Trace the full Collatz sequence for any positive integer, showing every step until the sequence reaches 1.
Euler's Totient Function Calculator
Computes Euler's totient φ(n), the count of integers from 1 to n that share no common factor with n.
Chinese Remainder Theorem Calculator
Finds the smallest non-negative integer x satisfying a system of two or three simultaneous modular congruences.
Quadratic Residue Calculator
Determines whether an integer a is a quadratic residue or non-residue modulo a prime p using Euler's criterion.
Prime Gap Analyzer
Scans a user-defined range of integers, identifies all primes, and computes the gaps between consecutive primes including maximum, minimum, and average gap.
Quadratic Residues Calculator
Computes the Legendre symbol (a/p) for any integer a and odd prime p, classifying a as a quadratic residue (+1), non-residue (−1), or zero (0).
Linear Diophantine Equation Solver
Finds all integer solutions to a linear Diophantine equation of the form ax + by = c.
Pythagorean Triples Generator
Generates all Pythagorean triples (a, b, c) satisfying a² + b² = c² up to a chosen limit, classifying each as primitive or non-primitive.
Prime Factorization Calculator
Breaks any positive integer into its unique product of prime factors, displayed as a multiplication string or using exponent notation.
Modular Arithmetic Calculator
Computes modular addition, multiplication, and exponentiation of integers under a chosen modulus.
Fibonacci Sequence Calculator
Generates Fibonacci sequences with custom starting values and computes the nth term or cumulative sum using Binet's formula.
Chinese Remainder Theorem Solver
Find the unique integer that satisfies multiple simultaneous modular congruences.
Perfect Number Analyzer
Check whether a number is perfect, abundant, or deficient by comparing it to the sum of its proper divisors.
Euler's Totient Function Calculator
Compute Euler's totient φ(n), the count of integers from 1 to n that share no common factor with n.
Quadratic Residue Calculator
Determine whether an integer a is a quadratic residue modulo a prime p, and compute the Legendre symbol (a/p).
Collatz Conjecture Analyzer
Trace the Collatz sequence from any starting integer — halving evens and applying 3n+1 to odds — until reaching 1.
Divisibility Rules Checker
Instantly check whether a number is divisible by 2–13 or a custom divisor, with plain-English explanations of each rule.
Perfect Number Checker
Determine whether a number is perfect, abundant, or deficient by summing its proper divisors.
Chinese Remainder Theorem Solver
Solve systems of simultaneous modular congruences using the Chinese Remainder Theorem (CRT).
Collatz Conjecture Calculator
Trace the full Collatz sequence for any starting integer and count the steps to reach 1.
Divisibility Test Calculator
Test whether a specific number is divisible by a chosen divisor, or count all divisors up to a custom limit.
Pascal's Triangle Calculator
Generate rows of Pascal's triangle or look up any individual binomial coefficient C(n, k).