Number Theory Tools
Prime factorization, GCF, LCM, Roman numerals, number names, and divisibility tools.
Prime Factorization Calculator
Decompose any positive integer into its unique prime factor expansion (Fundamental Theorem of Arithmetic) with visual factor trees and divisibility steps.
GCF Calculator
Find the Greatest Common Factor (GCF / GCD / HCF) of two or more numbers using Euclidean division algorithm steps, prime factorization, and common divisors.
LCM Calculator
Calculate the Least Common Multiple (LCM) of two or more integers with prime factorization tables, list of multiples, and Euclidean GCF connections.
Base Converter
Synchronously convert numbers between Binary (Base 2), Decimal (Base 10), Hexadecimal (Base 16), Octal (Base 8), and arbitrary radix bases 2–36.
Significant Figures Calculator
Count significant figures and round numbers to the correct number of sig figs.
Rounding Calculator
Round numbers to the nearest tens, hundreds, thousands, decimals, or significant figures.
Binary Converter
Convert decimal numbers to binary representation and vice-versa.
Hexadecimal Converter
Convert numbers between decimal, binary, and hexadecimal formats.
Roman Numerals Converter
Convert standard arabic numbers to ancient Roman numerals and vice-versa.
Divisibility Calculator
Check if a number is divisible by other integers and view applicable division rules.
Number Names Converter
Spell out numbers in English words (e.g. 142 to "one hundred forty-two").
Prime Number Checker
Verify if a number is prime, composite, or neither, with dynamic divisor scanning.
Digital Root Calculator
Calculate the digital root (iterative sum of digits) of a positive integer.
GCF and LCM Calculator
Calculate both the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of multiple integers.
Magic Square Calculator
Generate a magic square grid of size 3x3, 4x4, or 5x5.
Modular Multiplicative Inverse Calculator
Find the multiplicative inverse of an integer modulo n.
Relatively Prime Calculator
Determine if two numbers are relatively prime (coprime).
Triangular Numbers Calculator
Generate and calculate the n-th triangular number.
Fermat's Little Theorem Calculator
Demonstrate Fermat's Little Theorem for a base a and prime modulus p.
Power Mod Calculator
Calculate large powers modulo m (b^e mod m) using modular exponentiation.
Chinese Remainder Theorem Solver
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Chinese Remainder Theorem.
Common Multiples Finder
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Common Multiples Finder.
Continued Fraction Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Continued Fraction.
Common Factors Calculator | Find Common Factors of Numbers
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Common Factors | Find Common Factors of Numbers.
Derangement Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Derangement.
Congruence Modulo Checker
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Congruence Modulo Checker.
Combination Calculator | Calculate Combinations Easily
Free online Combination Calculator | Calculate Combinations Easily with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Combination with Repetition Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Combination with Repetition.
Clock Arithmetic Modulo Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Clock Arithmetic Modulo.
Divisibility Test - Check if a Number is Divisible by Another
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Divisibility Test - Check if a Number is Divisible by Another.
Greatest Common Factor (GCF) Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Greatest Common Factor (GCF).
Euclidean Algorithm Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Euclidean Algorithm.
Decimal to Binary Converter
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Decimal to Binary.
LCM Calculator: Find Least Common Multiple Online
Free online LCM Calculator: Find Least Common Multiple Online with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Factors of a Number Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Factors of a Number.
Factorial Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Factorial.
Factor Finder: Quickly Find Factors of Any Number
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Factor Finder: Quickly Find Factors of Any Number.
Factor Calculator: Find Factors of a Number
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Factor: Find Factors of a Number.
Irrational Number Comparator - Compare Irrational Numbers Online
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Irrational Number Comparator - Compare Irrational Numbers Online.
Greatest Common Factor (GCF) Calculator
Free online Greatest Common Factor (GCF) Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Linear Congruence Solver
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Linear Congruence.
Divisor with Remainder Finder | Math Tool
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Divisor with Remainder Finder | Math.
Modular Addition Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Modular Addition.
Irrational Number Generator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Irrational Number.
Modulo Calculator | Find Remainder of Division
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Modulo | Find Remainder of Division.
LCM Calculator: Find the Least Common Multiple Online
Free online LCM Calculator: Find the Least Common Multiple Online with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Modular Inverse Calculator | Find Inverse Modulo
Free online Modular Inverse Calculator | Find Inverse Modulo with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Is it a Prime Number? - Online Prime Checker
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Is it a Prime Number? - Online Prime Checker.
Divisibility Checker - Find Remainder & Check Divisibility
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Divisibility Checker - Find Remainder & Check Divisibility.
Modular Subtraction Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Modular Subtraction.
Modular Multiplication Calculator
Free online Modular Multiplication Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Permutation Calculator
Free online Permutation Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Next Multiple Calculator | Find the Next Multiple
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Next Multiple | Find the Next Multiple.
Irrational Number Checker - Is it Irrational?
Free online Irrational Number Checker - Is it Irrational? with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Prime Number List Generator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Prime Number List.
Prime Number Checker
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Prime Number Checker.
Number of Factors Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Number of Factors.
Pi Digit Calculator - Calculate First N Digits of Pi
Free online Pi Digit Calculator - Calculate First N Digits of Pi with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Sum of Factors Calculator
Free online Sum of Factors Calculator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Order of Element Modulo n Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Order of Element Modulo n.
Sum of Squares Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Sum of Squares.
Ten Thousands Place Value Calculator: Find the Digit
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Ten Thousands Place Value: Find the Digit.
Integer Partition Calculator: Find Number of Partitions
Free online Integer Partition Calculator: Find Number of Partitions with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Irrational Number Generator - Generate Pi Based Irrational Numbers
Free online Irrational Number Generator - Generate Pi Based Irrational Numbers with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Square Number List Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Square Number List.
Place Value Decomposition Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Place Value Decomposition.
Modular Exponentiation Calculator | EasyMaths
Free online Modular Exponentiation Calculator | EasyMaths with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Multinomial Coefficient Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Multinomial Coefficient.
Sum of Positive Integers Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Sum of Positive Integers.
Quadratic Congruence Solver
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Quadratic Congruence.
Permutation Calculator - Calculate Permutations Online
Free online Permutation Calculator - Calculate Permutations Online with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Pi Approximator
Free online Pi Approximator with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Prime Factor Calculator: Find Factors Easily
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Prime Factor: Find Factors Easily.
Perfect Number Checker
Free online Perfect Number Checker with step-by-step mathematical solutions, formulas, worked examples, and interactive calculator.
Cube Number List Calculator - Generate Cube Numbers Online
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Cube Number List - Generate Cube Numbers Online.
Golden Ratio Calculator - Visualize Phi & Fibonacci Sequence
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Golden Ratio - Visualize Phi & Fibonacci Sequence.
Number of Digits in 10^x | Power of 10 Digit Calculator
Analyze prime factors, divisibility congruences, modular arithmetic, and integer properties for Number of Digits in 10^x | Power of 10 Digit.
Number Theory Calculators and Tools
Number theory is one of the oldest and most fascinating branches of pure mathematics, devoted to the study of integers and their properties. From the ancient Greeks who first proved there are infinitely many prime numbers, to modern cryptographers who use prime factorization to secure internet communications, number theory is both deeply theoretical and practically essential.
Explore the Properties of Numbers
Our number theory calculators help you investigate the fundamental building blocks of mathematics — prime numbers, factors, multiples, and divisibility. These tools are invaluable for students learning foundational math concepts and for anyone who needs quick factor analysis.
Available Number Theory Tools
- Prime Factorization: Decompose any integer into its unique product of prime factors using trial division, with a step-by-step breakdown of each division.
- GCF Calculator (Greatest Common Factor): Find the largest number that divides evenly into two or more integers, essential for simplifying fractions and solving ratio problems.
- LCM Calculator (Least Common Multiple): Determine the smallest number that is a multiple of two or more integers, critical for adding fractions with unlike denominators and scheduling problems.
- Roman Numeral Converter: Convert between Arabic numerals and Roman numerals for historical dates, clock faces, and formal numbering systems.
- Number to Words: Convert numerical values into their English word equivalents for check writing, legal documents, and formal correspondence.
- Divisibility Checker: Test whether one number divides evenly into another and learn the divisibility rules for common factors.
Number theory powers real-world applications including RSA encryption (which secures online banking), error-correcting codes in data transmission, and hash functions used in computer science. Our free tools make these concepts accessible for learning and practical use.