Prime numbers, GCD, LCM, and divisibility calculators. Browse our free number theory tools below — all calculators are instant, accurate, and require no sign-up.
Complex Number a+bi Calculator — Perform operations on complex numbers in a+bi form — add, subtract, multiply, divide, conjugate, modulus, and argument with an interactive Argand diagram.
AND Calculator – Logical & Bitwise AND — Compute logical AND and bitwise AND for up to 4 inputs — see truth tables, bit-by-bit visualization, binary/hex output, and Boolean algebra laws.
Babylonian Number Calculator – Base-60 & Cuneiform Converter — Convert decimal numbers to Babylonian base-60 (sexagesimal) notation with cuneiform symbols, positional breakdown, and conversion tables showing the legacy of base-60 in modern time and angles.
Chinese Remainder Calculator — Solve systems of 2 or 3 congruences with the Chinese Remainder Theorem. Normalize residues, merge non-coprime systems, verify every modulus, and list the full solution family.
Bitwise Operations Calculator – AND, OR, XOR, NOT, Shifts — Perform all bitwise operations (AND, OR, XOR, NOT, NAND, NOR, XNOR, shifts) on two numbers with step-by-step binary breakdown, bit grid visualization, and operations comparison table.
Chord Length Calculator — Calculate chord length, arc length, sagitta, segment area, and sector area from radius and central angle, with circle diagram, reference table, and visual comparison bars.
Collatz Conjecture Calculator — Explore the Collatz conjecture (3n+1 problem) for any starting number. See total steps, max value, stopping time, full sequence table, step chart visual, and preset examples.
Common Denominator Calculator — Find the common denominator for two or more fractions, convert to equivalent fractions, compare values, and see step-by-step LCD solutions with visual fraction bars.
Complex Number to Polar Form Converter — Convert complex numbers between rectangular (a+bi), polar (r∠θ), Euler (re^iθ), and trigonometric forms with step-by-step conversion and a unit-circle diagram.
Corner Point Calculator — Find corner points of a feasible region from a system of linear inequalities, evaluate an objective function at each vertex, and identify the optimal solution for linear programming problems.
Coordinate Grid Calculator — Plot points on a coordinate grid, calculate distances, midpoints, slopes, areas, and identify quadrants. Includes SVG grid display, pairwise distance table, and presets.
Cylindrical Coordinates Calculator — Convert between cylindrical (r, θ, z) and Cartesian (x, y, z) coordinates with step-by-step solutions, reference angle table, and top-down projection visual.
Divisibility Test Calculator — Test divisibility of any number by 2–12 and custom divisors. See rules, digit sum method, remainder, comprehensive rules table, visual divisibility grid, and presets.
Divisor Calculator — Find all divisors of a number, count them (τ), sum them (σ), classify as perfect/abundant/deficient, visualize factor pairs, and explore presets with a comprehensive divisors table.
Euclidean Algorithm Calculator — Compute GCD via the Euclidean algorithm with step-by-step division, extended Euclidean algorithm, Bézout coefficients, LCM, presets, steps table, and visual representation.
Fermat's Little Theorem Calculator — Verify Fermat's little theorem, compute a^(p-1) mod p, perform modular exponentiation, check primality, view computation steps, and explore theorem properties with presets.
Fibonacci Sequence Calculator — Compute the nth Fibonacci number, generate a sequence of terms, explore golden ratio convergence, Binet's formula, presets, sequence table, and ratio convergence visual.
Greatest Common Denominator Calculator — Find the GCD of fraction denominators, simplify fractions, explore prime factorizations, and visualize the relationship between GCD and LCD with step-by-step solutions.
Greatest Common Divisor (GCD) Calculator — Calculate the GCD using the Euclidean algorithm and prime factorization. See Bézout identity, coprimality check, factor Venn diagram, and step-by-step solutions.
Least Common Denominator Calculator — Calculate the LCD for fractions using prime factorization or listing multiples. Convert fractions, compare visually, and see step-by-step solutions with factor tables.
Lowest Common Denominator Calculator — Find the lowest common denominator, add or subtract fractions, compare with visual fraction strips, and follow step-by-step solutions for any pair of fractions.
NOR Calculator – Logical & Bitwise NOR Gate — Compute logical NOR and bitwise NOR, see truth tables, universal gate proofs (build AND/OR/NOT from NOR), bit-by-bit visualization, and multi-input NOR.
OR Calculator – Logical & Bitwise OR / XOR — Compute inclusive OR and exclusive OR (XOR) for up to 4 inputs — see truth tables, bit-by-bit visualization, binary/hex output, and Boolean algebra laws.
Point-Slope Form Calculator — Convert between point-slope, slope-intercept, and standard form. Find the equation of a line from two points, parallel lines, and perpendicular lines with visual plots and comparison tables.
Polar Form Operations Calculator — Multiply, divide, raise to powers, and extract roots of complex numbers in polar form using De Moivre's theorem with an interactive polar plot.
Queueing Theory Calculator — Analyze queueing systems with M/M/1, M/M/c, and M/M/1/K models. Calculate utilization, average queue length, wait time, system time, probability of empty system, and more. Includes preset...
Relatively Prime Calculator — Check if two or more numbers are relatively prime (coprime), see Euclidean algorithm steps, prime factorizations, totient values, and coprimality grids.
Spherical Coordinates Calculator — Convert between spherical (ρ, θ, φ), Cartesian (x, y, z), and cylindrical (r, θ, z) coordinates with step-by-step solutions, convention toggle, and projection diagrams.
Tensor Product (Kronecker Product) Calculator — Compute the tensor (Kronecker) product of two matrices with step-by-step block decomposition, heatmap visualization, dimension analysis, and property verification table.
Ugly Duckling Theorem Calculator — Explore the Ugly Duckling Theorem with binary feature vectors. Compare objects using Hamming distance, shared features, Jaccard similarity, and matching coefficients. Includes preset examples, feat...
Truth Table Generator — Generate truth tables for logical expressions with up to 4 variables — AND, OR, NOT, XOR, NAND, NOR, IMPLIES, and XNOR — with tautology/contradiction detection and a visual result grid.
XOR Calculator – Logical & Bitwise Exclusive OR — Compute logical XOR and bitwise XOR for up to 4 inputs — see truth tables, parity checks, bit-by-bit visualization, binary/hex output, and swap tricks.