Starlight Tools directory

Number Theory Calculators

18 free, browser-based tools. No account required.

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Explore integer structure, factors, divisibility, and prime decomposition with private browser-based number theory calculators. Start with the Prime Number Generator, Prime Factorization Calculator, or LCM & GCF Calculator.

Yellow star mascot arranging the same integer into distinct number partitions

Integer Partition Calculator and Partition Generator

Calculate p(n) exactly, generate unique unordered sums for practical sizes, and copy or download the complete results. v1.0

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Yellow star mascot representing an integer as a sum of two squares

Sum of Two Squares Calculator and Representation Finder

Check whether n = a² + b², list every unique nonnegative pair, and verify the prime-factor condition. v1.0

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Yellow star mascot comparing record-setting divisor counts

Highly Composite Number and Divisor Record Finder

Find every number through an exact limit that sets a new positive-divisor record, with τ values, prime factorizations, and CSV export. v1.0

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Yellow star mascot solving a Pell equation with integer values

Pell Equation Solver for Integer Solutions

Solve x² − Dy² = 1 using continued fractions, then list and verify the fundamental and successive positive integer solutions. v1.0

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Yellow star mascot finding quadratic residues and modular square roots

Quadratic Residue and Legendre Symbol Calculator

Calculate (a/p), classify quadratic residues, apply Euler’s criterion, and find both modular square roots. v1.0

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Yellow star mascot calculating the Möbius and Mertens functions

Möbius Function and Mertens Function Calculator

Calculate μ(n), M(n), square-free status, prime factors, summatory counts, and nearby sequence values. v1.0

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Yellow star mascot comparing perfect, abundant, and deficient numbers

Perfect, Abundant and Deficient Number Checker

Classify a positive integer from its proper-divisor sum, with prime factorization, exact steps, and the complete divisor list. v1.0

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$Yellow star mascot building a continued fraction and rational approximation$

Continued Fraction Calculator and Rational Approximation Tool

Expand a fraction or finite decimal, inspect exact convergents, and find the closest fraction within a denominator limit. v1.0

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Yellow star mascot solving a linear Diophantine equation over the integers

Linear Diophantine Equation Solver with Integer Solutions

Solve ax + by = c over the integers, test existence, and find one exact pair plus the complete parameterized family. v1.0

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Yellow star mascot applying a digit-sum divisibility test

Divisibility Test Calculator with Rules and Steps

Test any integer and nonzero divisor, then see the exact quotient, remainder, applicable shortcut rule, and worked steps. v1.0

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Yellow star mascot checking that two numbers are coprime

Coprime Number Checker & Pairwise Coprime Calculator

Check a pair or list for coprimality, compare pairwise and collective GCD, and identify every conflicting pair. v1.0

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Yellow star mascot finding a GCD and Bézout coefficients

Extended Euclidean Algorithm Calculator

Find the GCD and exact Bézout coefficients, verify the identity, and follow every Euclidean division step. v1.0

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Yellow star mascot identifying integers coprime to 12 for Euler's totient

Euler’s Totient Function Calculator with Steps

Calculate φ(n) with prime factorization, Euler’s product formula, exact steps, and small coprime lists. v1.0

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Yellow star mascot counting and summing the positive divisors of 12

Divisor Count and Sum of Divisors Calculator

Calculate τ(n), σ(n), proper-divisor sums, classification, and complete positive-divisor lists with exact steps. v1.0

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Yellow star mascot filtering prime numbers through a sieve

Prime Number Generator & Sieve Calculator

Generate primes in an inclusive range, inspect a sieve chart, and copy or download exact results. v1.0

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Prime Factorization Calculator

Find prime factors, exponent form, factor pairs, divisors, a factor tree, and trial-division steps. v1.0

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Common Factor Calculator

List the common factors and greatest common factor of two or more integers with Euclidean steps. v1.0

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LCM and GCF calculator displaying factors and results

LCM & GCF Calculator

Find the least common multiple and greatest common factor using several step-by-step methods. v1.0

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About These Number Theory Calculators

These calculators examine the factors, multiples, divisibility, and prime structure of integers. They provide exact results and explanatory methods suitable for learning, checking work, and computational exploration.