number theory Calculators
GCD Calculator
Find the largest integer that divides two numbers exactly with no remainder. Use it to simplify fractions, reduce ratios, or solve number-theory problems.
LCM Calculator
Find the smallest positive integer divisible by both of two given numbers. Useful for adding fractions, scheduling repeating events, and aligning cycles.
Prime Number Checker
Instantly determine whether any positive integer is a prime number. Use it for number-theory homework, cryptography key checks, or satisfying mathematical curiosity.
Factorial Calculator
Compute the product of all positive integers up to a given number (n!). Essential for permutations, combinations, probability, and series expansion calculations.
Fibonacci Calculator
Find the exact Fibonacci number at any position in the sequence. Use it to explore mathematical patterns, check algorithm results, or apply Fibonacci ratios in design.
Modular Arithmetic Calculator
Compute modular addition, subtraction, and multiplication instantly. Use it in cryptography, competitive programming, or number theory to keep results within a fixed range.
Perfect Number Checker
Instantly check whether any positive integer is a perfect number — one that equals the sum of its proper divisors. Useful for number theory study and math competitions.
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. Essential for RSA key generation and number theory problems.
Divisor Count Calculator
Count exactly how many divisors a positive integer has, including 1 and itself. Useful for number theory, factorization analysis, and competition math.
Binary to Decimal Converter
Convert any binary (base-2) number to its decimal (base-10) equivalent in one click. Handy for programming, digital electronics, and computer science coursework.
Prime Factorization Calculator
Break any integer into its prime building blocks instantly. Use this when simplifying fractions, finding GCDs, or verifying primality. Results display as a product or exponent form.
GCD and LCM Calculator
Instantly compute the Greatest Common Divisor and Least Common Multiple of two integers. Ideal for simplifying fractions, scheduling repeating events, or solving ratio problems.
Fibonacci Sequence Calculator
Calculate any Fibonacci number by position or generate the full sequence up to a given term. Useful for algorithm study, mathematical modeling, and exploring the golden ratio.
Perfect Number Calculator
Determine whether any integer is perfect, abundant, or deficient based on its proper divisor sum. Use it to explore number theory or verify known perfect numbers like 6 and 28.
Collatz Conjecture Calculator
Trace the full Collatz sequence for any positive integer, showing every step until the sequence reaches 1. Ideal for visualizing the 3n+1 problem and analyzing stopping times.
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. Essential for RSA encryption key generation and modular arithmetic problems.
Chinese Remainder Theorem Calculator
Finds the smallest non-negative integer x satisfying a system of two or three simultaneous modular congruences. Used in cryptography, scheduling problems, and number theory proofs.
Quadratic Residue Calculator
Determines whether an integer a is a quadratic residue or non-residue modulo a prime p using Euler's criterion. Useful in number theory, cryptography, and primality testing.
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. Ideal for exploring prime distribution patterns.
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). Useful for modular arithmetic and cryptographic analysis.
Linear Diophantine Equation Solver
Finds all integer solutions to a linear Diophantine equation of the form ax + by = c. Use it when you need exact integer answers in problems involving divisibility, coin combinations, or scheduling.
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. Useful for geometry problems, number theory study, and competition math.
Prime Factorization Calculator
Breaks any positive integer into its unique product of prime factors, displayed as a multiplication string or using exponent notation. Ideal for simplifying fractions, finding GCDs, LCMs, and studying number theory.
Modular Arithmetic Calculator
Computes modular addition, multiplication, and exponentiation of integers under a chosen modulus. Essential for cryptography, clock arithmetic, hash functions, and competitive programming problems.
Fibonacci Sequence Calculator
Generates Fibonacci sequences with custom starting values and computes the nth term or cumulative sum using Binet's formula. Use it for math coursework, algorithm analysis, or exploring the golden ratio.
Chinese Remainder Theorem Solver
Find the unique integer that satisfies multiple simultaneous modular congruences. Use this when solving scheduling puzzles, cryptographic problems, or any system where a number must leave specific remainders under different divisors.
Perfect Number Analyzer
Check whether a number is perfect, abundant, or deficient by comparing it to the sum of its proper divisors. Use it to explore number theory properties or scan a range of integers for perfect numbers.
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. Essential for RSA key generation, modular arithmetic, and exploring multiplicative number theory.
Quadratic Residue Calculator
Determine whether an integer a is a quadratic residue modulo a prime p, and compute the Legendre symbol (a/p). Used in number theory, primality testing, and cryptographic algorithm design.
Collatz Conjecture Analyzer
Trace the Collatz sequence from any starting integer — halving evens and applying 3n+1 to odds — until reaching 1. Reveals stopping time, maximum value reached, and sequence statistics for the famous unsolved 3n+1 problem.
Divisibility Rules Checker
Instantly check whether a number is divisible by 2–13 or a custom divisor, with plain-English explanations of each rule. Ideal for students learning number theory or anyone verifying factors quickly.
Perfect Number Checker
Determine whether a number is perfect, abundant, or deficient by summing its proper divisors. Use it when studying number theory, checking homework, or exploring classic mathematical puzzles.
Chinese Remainder Theorem Solver
Solve systems of simultaneous modular congruences using the Chinese Remainder Theorem (CRT). Essential for cryptography, competitive programming, and advanced number-theory coursework.
Collatz Conjecture Calculator
Trace the full Collatz sequence for any starting integer and count the steps to reach 1. Perfect for exploring one of mathematics' most famous unsolved problems visually and numerically.
Divisibility Test Calculator
Test whether a specific number is divisible by a chosen divisor, or count all divisors up to a custom limit. Useful for simplifying fractions, factoring integers, and classroom exercises.
Pascal's Triangle Calculator
Generate rows of Pascal's triangle or look up any individual binomial coefficient C(n, k). Useful for combinatorics, probability problems, and expanding binomial expressions quickly.