Number Tools
Browse all available number tools.
Available tools
- Abundant Number Checker Check whether the sum of the proper divisors of a positive integer exceeds the integer.
- Aliquot Sum Calculator Compute the sum of proper divisors of n excluding n itself.
- Aliquot Sum Practice Create reproducible practice for Aliquot Sum Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Amicable Pair Checker Check whether two integers form an amicable pair of proper divisor sums.
- Armstrong Number Checker Check whether a nonnegative integer equals the sum of its digits each raised to the digit count.
- Automorphic Number Checker Check whether the square of a nonnegative integer ends with the integer itself.
- Balanced Ternary Single Digit Carry Tool Calculate balanced ternary single digit carry from explicit caller-supplied inputs.
- Balanced Ternary Single Digit Value Tool Compute balanced ternary single digit value from explicit bounded inputs.
- Betrothed Numbers Checker Check whether two integers form a pair of betrothed numbers whose proper divisor sums exceed each partner by one.
- Bijective Radix One Digit Borrow Tool Calculate bijective radix one digit borrow from explicit caller-supplied inputs.
- Binary Fraction Grid Step Return an exact binary fraction grid step as integer strings, including the unit step at zero fractional bits.
- Binary Radix Exponent Gap Tool Calculate binary radix exponent gap from explicit caller-supplied inputs.
- Catalan Number Checker Check whether a nonnegative safe integer is a Catalan number generated with the exact recurrence C(k+1) = C(k) * 2(2k+1) / (k+2).
- Chinese Remainder Theorem Solver Solve a list of integer congruences, including non-coprime moduli when consistent; return the smallest nonnegative solution and its period as exact decimal strings.
- Continued Fraction Convergent Determinant Tool Calculate continued fraction convergent determinant from explicit caller-supplied inputs.
- Continued Fraction Expander Find the finite simple continued-fraction coefficients of a rational number by Euclidean division, including correct floor behavior for negative numerators.
- Coprime Count Calculator Count the positive integers up to a positive integer that are coprime to it (Euler totient).
- Coprime Count Practice Create reproducible practice for Coprime Count Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Coprime Number Checker Check whether two nonzero safe integers share no factor greater than one.
- Decimal Double Rounding Witness Tool Demonstrate explicit Math.round half-toward-positive-infinity decimal rounding; this tool intentionally compares rounding policies.
- Decimal Exponent Spelling Compactor Compact an exact finite decimal spelling into canonical scientific notation without numeric parsing.
- Decimal Exponent Spelling Expander Expand finite decimal exponent notation exactly to plain text with the explicit source scale retained.
- Decimal Negative Zero Policy Apply an explicit negative-zero spelling policy without treating negative zero as a different numerical value.
- Decimal Place Carry Cascade Count Tool Increment a nonnegative decimal digit string while retaining its minimum width and counting trailing-nine carries.
- Decimal Quantum Membership Exact decimal quantum membership; signed arithmetic uses floor rather than truncation.
- Decimal Quantum Neighbor Values Exact decimal quantum bounding neighbors; signed arithmetic uses floor rather than truncation.
- Decimal Rounding Error Fraction Exact decimal quantum rounding error with ties toward positive infinity; signed arithmetic uses floor rather than truncation.
- Decimal Scale Alignment Zero Count Tool Compute decimal scale alignment zero count from explicit bounded inputs.
- Decimal Significant Digit Count Count spelling-defined significant digits with an explicit integer-trailing-zero policy; decimal trailing zeros count and all-zero text counts as one.
- Decimal Spelling Exact Comparison Compare finite decimal spellings exactly using BigInt scale alignment, not IEEE-754 conversion.
- Decimal Spelling Scale Aligner Align a list of decimal spellings to a common exact coefficient scale; no precision loss or rounding.
- Decimal Spelling Scale Profiler Profile exact decimal spelling as integer coefficient and decimal scale, including exponent and negative-zero evidence.
- Decimal Spelling Zero Trimmer Canonicalize a decimal spelling by removing fractional trailing zeros and integer leading zeros; negative zero becomes zero.
- Decimal Tie Rounding Classifier Exact decimal quantum half-tie classification; signed arithmetic uses floor rather than truncation.
- Decimal Tie To Even Parity Flag Tool Calculate decimal tie to even parity flag from explicit caller-supplied inputs.
- Decimal Ulp At Explicit Exponent Tool Return decimal spacing at a supplied base-ten order and significant-digit count, not binary IEEE spacing.
- Digit Count Calculator Count the base-10 digits of an integer without counting its sign or leading zeros. Enter long integers as decimal text to preserve every digit; safe numeric inputs are also accepted. Zero has one digit.
- Digit Frequency Counter Count how many times each digit appears in a nonnegative integer.
- Digit Reversal Fixed Point Tool Compare a fixed-width uppercase digit string to its reversal, preserving leading zeroes.
- Digit Sum Calculator Sum the base-10 digits of a safe integer.
- Digital Root Calculator Calculate the repeated base-10 digit sum of a safe integer.
- Divisibility Checker Check whether one safe integer is evenly divisible by another.
- Divisor Count Calculator Count the positive divisors of a positive integer via its prime factorization.
- Divisor Count Practice Create reproducible practice for Divisor Count Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Divisor Pair Square Duplication Check Tool Calculate divisor pair square duplication check from explicit caller-supplied inputs.
- Divisor Sum Calculator Sum the positive divisors of a positive integer via its prime factorization.
- Divisor Sum Practice Create reproducible practice for Divisor Sum Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Egyptian Fraction Expander Expand a positive rational number into an integer part and distinct unit fractions using the greedy algorithm; output may have large denominators.
- Emirp Checker Check whether a prime integer yields a different prime when its digits are reversed.
- Euclidean Remainder One Step Bound Tool Calculate euclidean remainder one step bound from explicit caller-supplied inputs.
- Euler Totient Calculator Compute Euler's totient function φ(n).
- Evil Number Checker Check whether a nonnegative integer has an even count of one bits in binary.
- Fibonacci Number Checker Check whether a nonnegative safe integer is a Fibonacci number.
- Fixed Point Add Overflow Flag Add exact raw fixed-point integers and flag explicit signed or unsigned word overflow; does not wrap or saturate.
- Fixed Point Division and Rescale Exact raw fixed-point division and rescaling, truncating toward zero while retaining signed remainder evidence.
- Fixed Point Integer Decoder Decode an exact binary fixed-point integer to terminating decimal text with explicit fractional bit count.
- Fixed Point Integer Encoder Encode exact decimal text on a binary fixed-point grid; rejects values requiring rounding.
- Fixed Point Multiply and Rescale Exact raw fixed-point multiplication and rescaling, truncating toward zero while retaining signed remainder evidence.
- Fixed Point Range Envelope Report the exact representable rational envelope of a signed or unsigned binary fixed-point word; no floating approximation.
- Fixed Point Saturation Result Saturate an exact fixed-point raw integer to an explicit word range, retaining whether clipping occurred.
- Greatest Common Factor Calculator Calculate the greatest common factor, also known as the greatest common divisor, of two safe integers.
- Happy Number Checker Check whether repeated sums of squared digits reach one rather than entering a cycle.
- Harshad Number Checker Check whether a positive integer is divisible by the sum of its digits.
- Heron's Square Root Method Approximate the nonnegative square root with Heron's iteration and stop when successive estimates meet a relative tolerance.
- Heron's Square Root Method Practice Create reproducible practice for Heron's Square Root Method from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Hexagonal Number Checker Check whether a nonnegative integer is a hexagonal number k(2k-1).
- Integer Canonical Sign Token Tool Normalize the sign and magnitude of an exact signed decimal integer, including signed or padded zero.
- Integer Ceiling Division Sign Case Tool Calculate integer ceiling division sign case from explicit caller-supplied inputs.
- Integer Division Zero Remainder Sign Tool Label exact integer remainder conventions, preserving dividend-signed zero metadata for truncation.
- Integer Euclidean Quotient Sign Case Tool Compute integer euclidean quotient sign case from explicit bounded inputs.
- Integer Floor Ceiling Bracket Pair Return explicit real-value floor and ceiling brackets, rejecting outputs outside safe integer range.
- Integer Multiple Nearest Lower Upper Tool Compute integer multiple nearest lower upper from explicit bounded inputs.
- Integer Nearest Multiple Tie Policy Tool Calculate integer nearest multiple tie policy from explicit caller-supplied inputs.
- Integer Negabinary Digit Parity Tool Count the ones and digit length in the canonical base −2 expansion, including one zero digit for zero.
- Integer Parity Checker Identify whether a safe integer is even or odd.
- Integer Parity Last Digit Witness Tool Use the final decimal magnitude digit as an exact parity witness for a bounded arbitrary-precision integer.
- Integer Perfect Power Parity Witness Tool Calculate integer perfect power parity witness from explicit caller-supplied inputs.
- Integer Radical Exponent Tool Reduce supplied nonnegative prime-factor exponents to squarefree radical exponents; primality of the implicit bases is caller supplied.
- Integer Radix Negative Zero Policy Tool Format a safe integer in radix 2–36 with an explicit direct-call negative-zero policy.
- Integer Safe Addition Margin Tool Report exact decimal-string positive and negative addition margins around a safe integer, including margins larger than the safe-integer range.
- Integer Signum Zero Policy Tool Calculate integer signum zero policy from explicit caller-supplied inputs.
- Integer Square Bracket Containment Tool Calculate integer square bracket containment from explicit caller-supplied inputs.
- Integer Square Neighbor Gap Pair Tool Compute integer square neighbor gap pair from explicit bounded inputs.
- Kaprekar Number Checker Check whether a positive integer's square splits into a left part and a right part of the same digit count that sum back to the integer.
- Kaprekar Steps Calculator Apply the four-digit descending-minus-ascending digit routine with leading zeros until 6174 or zero, reporting every intermediate value.
- Lcm Overflow Safe Factor Order Tool Calculate lcm overflow safe factor order from explicit caller-supplied inputs.
- Leading Digit Extractor Extract the leading decimal digit of an integer, ignoring its sign.
- Leading Digit Extractor Practice Create reproducible practice for Leading Digit Extractor from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Least Common Multiple Calculator Calculate the nonnegative least common multiple of two safe integers.
- Lucas Number Checker Check whether a nonnegative safe integer equals a Lucas number L(0)=2, L(1)=1, ...
- Mersenne Number Checker Check whether a nonnegative safe integer equals 2^n - 1 for a positive integer n.
- Möbius Function Calculator Möbius μ(n): 0 when divisible by a square, (−1)^k with k distinct primes, μ(1)=1.
- Möbius Function Practice Create reproducible practice for Möbius Function Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Modular Exponentiation Calculator Compute base^exponent modulo a positive integer using repeated squaring and BigInt intermediates; handles negative bases without floating-point overflow.
- Modular Signed Residue Representative Tool Calculate modular signed residue representative from explicit caller-supplied inputs.
- Negative Radix One Division Step Tool Calculate negative radix one division step from explicit caller-supplied inputs.
- Negative Zero Signbit Preservation Label Label the supplied binary64 negative zero sign as text before portable numeric output canonicalization.
- Next Prime Calculator Smallest prime strictly greater than the given integer.
- Next Prime Practice Create reproducible practice for Next Prime Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Number Divisors Calculator All positive divisors of a positive integer, sorted ascending.
- Number: Factorial Trailing Zero Base Factor Term Tool Compute one Legendre prime valuation contribution to n! trailing zeros for an explicitly supplied prime factor and base multiplicity; does not factor a base.
- Number: Half Integer Tie Neighbor Pair Tool Report the integer neighbors and exact half-integer tie status of one safely bounded number without imposing a rounding policy.
- Number: Integer Digit Place Value Tool Extract an exact base-ten digit and unsigned place-value contribution from a signed integer, counting places from zero at units.
- Number: Modulus Symmetric Representative Tool Return the exact symmetric residue in [-m/2,m/2), choosing the negative representative at even-modulus ties.
- Number: Unsigned Word Maximum Decimal Digits Tool Determine exact maximum unsigned word value and required decimal display digits for a supplied bit width.
- Numeric Palindrome Checker Check whether the unsigned base-10 digits of a safe integer read the same in both directions.
- Pentagonal Number Checker Check whether a nonnegative safe integer equals k(3k-1)/2 for some integer k >= 1.
- Perfect Cube Checker Check whether a safe integer is an exact integer cube.
- Perfect Number Checker Check whether the sum of the proper divisors of a positive integer equals the integer.
- Perfect Square Checker Check whether a nonnegative safe integer is an exact integer square.
- Positional Digit Carry Single Column Tool Compute positional digit carry single column from explicit bounded inputs.
- Positional Digit Leading Zero Count Count leading zeros in explicit ASCII decimal digits while preserving the remaining digit text without numeric coercion.
- Positional Fraction Terminating Prime Support Tool Calculate positional fraction terminating prime support from explicit caller-supplied inputs.
- Prime Factorization Calculator Factor a positive integer at most one trillion by trial division; output lists prime factors with multiplicity. One has no prime factors.
- Prime Factorization One Exponent Contribution Tool Calculate prime factorization one exponent contribution from explicit caller-supplied inputs.
- Prime Number Checker Check whether a safe integer is prime using deterministic trial division.
- Pronic Number Checker Check whether a nonnegative integer equals the product of two consecutive integers.
- Radix Fraction Leading Zero Budget Count an explicit fractional digit string leading run of a supplied zero symbol without interpreting its radix.
- Radix Integer Single Digit Borrow Tool Calculate radix integer single digit borrow from explicit caller-supplied inputs.
- Radix Power Ceiling Digit Budget Tool Compute radix power ceiling digit budget from explicit bounded inputs.
- Radix Repeating Cycle Denominator Order Tool Find the repeating period of 1/denominator after removing factors shared with the radix.
- Rational Addition Denominator Lcm Factor Tool Calculate rational addition denominator lcm factor from explicit caller-supplied inputs.
- Rational Cross Product Comparison Sign Compare two explicit integer-text rationals exactly with denominator-sign correction and no floating-point conversion.
- Rational Dyadic Denominator Flag Tool Reduce a supplied exact rational before testing whether its denominator is a power of two.
- Rational Floor Ceiling Gap Tool Calculate rational floor ceiling gap from explicit caller-supplied inputs.
- Rational Mediant Denominator Budget Tool Calculate rational mediant denominator budget from explicit caller-supplied inputs.
- Rational Mediant Weighted Crosswalk Tool Compute rational mediant weighted crosswalk from explicit bounded inputs.
- Rational Power Sign Domain Flag Tool Calculate rational power sign domain flag from explicit caller-supplied inputs.
- Rational Reduced Denominator Grid Step Tool Compute rational reduced denominator grid step from explicit bounded inputs.
- Rational Repetend Pre Period Budget Tool Nonrepeating prefix length for a reduced rational denominator in the supplied radix; numerator must already be coprime.
- Rational Signed Denominator Crossproduct Order Tool Calculate rational signed denominator crossproduct order from explicit caller-supplied inputs.
- Rational Unit Fraction Complement Term Tool Compute rational unit fraction complement term from explicit bounded inputs.
- Reciprocal Integer Fraction Order Witness Tool Calculate reciprocal integer fraction order witness from explicit caller-supplied inputs.
- Reverse in Base Tool Reverse the digits of a nonnegative integer interpreted in a base between 2 and 36.
- Reverse in Base Tool Practice Create reproducible practice for Reverse in Base Tool from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Reverse Integer Digits Tool Reverse the base-10 digits of a safe integer while preserving its sign.
- Reverse Integer Digits Tool Practice Create reproducible practice for Reverse Integer Digits Tool from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Semiprime Checker Check whether a positive integer is the product of exactly two primes.
- Signed Remainder Convention Residual Tool Calculate signed remainder convention residual from explicit caller-supplied inputs.
- Smith Number Checker Check whether a composite number's digit sum equals the digit sum of its prime factors with multiplicity.
- Square-Free Checker Check whether no perfect square greater than one divides a positive integer.
- Trailing Zeros Counter Count the consecutive zero digits at the end of a nonnegative integer.
- Trailing Zeros Counter Practice Create reproducible practice for Trailing Zeros Counter from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.