Number Theory Calculators
Last updated: September 2026
Prime Factorization Calculator
Decompose any positive integer into its unique product of prime numbers — the fundamental "atomic" representation that underlies divisibility, fractions, modular arithmetic, and cryptography.
Prime Number Checker
Instantly determine whether any positive integer is a prime number.
GCD Calculator
Find the greatest common divisor — the largest integer that divides two whole numbers exactly with no remainder.
Chinese Remainder Theorem Solver
Find the unique integer that satisfies multiple simultaneous modular congruences.
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.
Perfect Number Analyzer
Check whether a number is perfect, abundant, or deficient by comparing it to the sum of its proper divisors.
Divisor Count Calculator
Count exactly how many divisors a positive integer has, including 1 and itself.
Linear Diophantine Equation Solver
Finds all integer solutions to a linear Diophantine equation of the form ax + by = c.
Fibonacci Sequence Calculator
Generates Fibonacci sequences with custom starting values and computes the nth term or cumulative sum using Binet's formula.
Fibonacci Calculator
Find the exact Fibonacci number at any position in the sequence, where each term is the sum of the two before it.
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.
Divisibility Test Calculator
Test whether a specific number is divisible by a chosen divisor, or count all divisors up to a custom limit.
LCM Calculator
Find the least common multiple — the smallest positive integer that two numbers both divide into evenly.
Collatz Conjecture Calculator
Trace the full Collatz sequence for any positive integer, showing every step until the sequence reaches 1.
Chinese Remainder Theorem Calculator
Finds the smallest non-negative integer x satisfying a system of two or three simultaneous modular congruences.
Modular Arithmetic Calculator
Computes modular addition, multiplication, and exponentiation of integers under a chosen modulus.
Binary to Decimal Converter
Convert any binary (base-2) number to its decimal (base-10) equivalent in one click.
GCD and LCM Calculator
Instantly compute the Greatest Common Divisor and Least Common Multiple of two integers.
Pascal's Triangle Calculator
Generate rows of Pascal's triangle or look up any individual binomial coefficient C(n, k).
Quadratic Residue Calculator
Determine whether an integer a is a quadratic residue modulo a prime p, and compute the Legendre symbol (a/p).
Divisibility Rules Checker
Instantly check whether a number is divisible by 2–13 or a custom divisor, with plain-English explanations of each rule.
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.
Factorial Calculator
Compute the factorial n!, the product of all positive integers up to n.