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Number Theory Calculators
Investigate primes, factors, divisibility, modular arithmetic, and integer properties. Use this collection when investigate primes, factors, divisibility, modular arithmetic, and integer properties. Start with the calculator matching the values you possess, then use related tools to verify or extend the result.
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Number Theory topics
Select a topic to reveal its calculators. Multiple topics can remain open at the same time.Number TheoryInvestigate primes, factors, divisibility, modular arithmetic, and integer properties.46 available
- GCF CalculatorFind the greatest common factor and, for two integers, a Bézout identity.Open calculator
- LCM CalculatorFind the conventional non-negative least common multiple of an integer list.Open calculator
- Prime Number CalculatorClassify an integer as prime, composite, or neither.Open calculator
- Prime Factorization CalculatorExpress a positive integer as a product of prime powers.Open calculator
- Factors CalculatorList every positive divisor of an integer.Open calculator
- Divisibility Test CalculatorCheck whether one integer divides another using the exact remainder.Open calculator
- Relatively Prime CalculatorCheck whether an integer list has greatest common factor 1.Open calculator
- Divisor Count & Sum CalculatorCalculate the number and sum of positive divisors from prime powers.Open calculator
- Sieve of Eratosthenes CalculatorGenerate every prime up to a bounded inclusive limit.Open calculator
- Next & Previous Prime CalculatorFind the closest prime strictly below and strictly above an integer.Open calculator
- Prime Counting Function CalculatorEvaluate π(x), the count of primes not exceeding an integer bound.Open calculator
- Miller-Rabin Primality Test CalculatorRun a deterministic primality classification over the full unsigned 64-bit range.Open calculator
- Modulo CalculatorFind the canonical non-negative Euclidean remainder.Open calculator
- Modular Arithmetic CalculatorAdd, subtract, multiply, or divide residue classes modulo n.Open calculator
- Power Mod CalculatorEvaluate a large non-negative integer power modulo n efficiently.Open calculator
- Inverse Modulo CalculatorFind an additive or multiplicative inverse modulo n.Open calculator
- Linear Congruence SolverSolve ax≡b (mod n) and list every residue-class solution.Open calculator
- Chinese Remainder Theorem CalculatorSolve a compatible list of congruences, including non-coprime moduli.Open calculator
- Multiplicative Order CalculatorFind the smallest positive k with aᵏ≡1 (mod n).Open calculator
- Primitive Root CalculatorFind the smallest generator of the multiplicative units modulo n when one exists.Open calculator
- Discrete Logarithm CalculatorFind the smallest non-negative x satisfying aˣ≡b (mod n).Open calculator
- Quadratic Residue & Modular Square Root CalculatorClassify a residue and list every x satisfying x²≡a (mod n).Open calculator
- Legendre & Jacobi Symbol CalculatorEvaluate a Legendre symbol for an odd prime or a Jacobi symbol for an odd positive denominator.Open calculator
- Linear Diophantine Equation CalculatorSolve ax+by=c over the integers or report that no solution exists.Open calculator
- Euler's Totient CalculatorCount positive integers through n that are coprime to n.Open calculator
- Fermat's Little Theorem CalculatorVerify aᵖ≡a (mod p) for a supplied prime p.Open calculator
- Euler's Theorem CalculatorVerify a^φ(n)≡1 (mod n) for coprime a and n.Open calculator
- Wilson's Theorem CalculatorClassify n using the exact factorial residue criterion.Open calculator
- Carmichael Function CalculatorFind the exponent λ(n) of the multiplicative unit group modulo n.Open calculator
- Möbius Function CalculatorEvaluate μ(n) from the prime factorization.Open calculator
- P-adic Valuation CalculatorCount the exponent of prime p in a nonzero integer n.Open calculator
- Perfect Number CalculatorTest whether the proper divisors of n sum exactly to n.Open calculator
- Abundant Number CalculatorClassify n as abundant, perfect, or deficient.Open calculator
- Amicable Number CalculatorTest whether two distinct integers are mutual aliquot sums.Open calculator
- Carmichael Number CalculatorTest a composite integer using Korselt's criterion.Open calculator
- Perfect Square CalculatorTest an arbitrary supported integer and report its integer square-root floor.Open calculator
- Perfect Cube CalculatorTest a positive or negative integer for an exact integer cube root.Open calculator
- Square-Free Number CalculatorCheck whether any prime square divides n.Open calculator
- Digital Root CalculatorReduce the absolute decimal digits of an integer to one digit.Open calculator
- Happy Number CalculatorFollow repeated decimal digit-square sums and classify the terminal cycle.Open calculator
- Kaprekar Number CalculatorTest the base-10 Kaprekar split using the digit length of n.Open calculator
- Armstrong Number CalculatorTest whether a non-negative integer equals the sum of its digits raised to its digit count.Open calculator
- Mersenne Number & Prime CalculatorCalculate Mₚ=2ᵖ−1 and test both the exponent and Mersenne number for primality.Open calculator
- Aliquot Sum & Sequence CalculatorCalculate the proper-divisor sum and iterate a bounded aliquot sequence.Open calculator
- Goldbach Partition CalculatorFind a pair of primes whose sum is the entered even integer.Open calculator
- Sum of Two Squares CalculatorFind non-negative integers a,b with n=a²+b² when they exist.Open calculator