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Free online factor calculator to find all factors, prime factors, factor pairs, and divisors of any number instantly. Calculate factors with detailed step-by-step solutions and prime factorization.
Factors of a number are whole numbers that divide evenly into that number without leaving a remainder. In other words, when you divide a number by one of its factors, you get another whole number as the result.
For example, the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24
Every number has at least two factors: 1 and itself. Numbers with exactly two factors are called prime numbers (like 2, 3, 5, 7, 11), while numbers with more than two factors are called composite numbers (like 4, 6, 8, 9, 10, 12).
Test each number from 1 up to the number itself to see if it divides evenly.
Only test numbers up to the square root of the number. For each divisor found, both it and the quotient are factors.
Find prime factors first, then generate all combinations to get all factors.
Prime factorization is the process of expressing a number as a product of prime numbers. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).
Prime factorization is useful for finding GCF and LCM, simplifying radicals and fractions, solving number theory problems, and understanding the structure of numbers.
Factor pairs are two numbers that multiply together to give the original number. Each factor pair shows a multiplication relationship.
Factor pairs are useful for understanding multiplication, solving area problems, factoring algebraic expressions, and finding rectangular arrangements of objects.
Use GCF of numerator and denominator to reduce fractions to lowest terms. Example: 24/36 = 2/3 (divide by GCF 12).
Divide items into equal groups. If you have 24 items, you can make groups of 1, 2, 3, 4, 6, 8, 12, or 24.
Find possible dimensions of rectangles. A rectangle with area 24 can be 1×24, 2×12, 3×8, or 4×6.
Determine tile sizes that fit perfectly. For a 24×36 area, use tiles that are factors of both dimensions.
Understanding prime and composite numbers, divisibility rules, and mathematical properties of integers.
Factoring polynomials, solving equations, and simplifying algebraic expressions using factorization.
Find greatest common factor
Find least common multiple
Simplify and calculate fractions
Advanced math operations
Calculate percentages easily
Simplify and calculate ratios
Calculate powers and exponents
Square root, cube root calculator
This factor calculator and educational content have been developed following standard mathematical principles and verified against authoritative sources including Khan Academy, Wolfram MathWorld, and academic mathematics curricula.
Last Updated: February 13, 2026 |Accuracy: Verified against standard mathematical algorithms
Comprehensive lessons on factors, prime factorization, and divisibility with practice problems
Visit Khan Academy →Mathematical definitions and properties of divisors and factors with advanced concepts
Visit MathWorld →Easy-to-understand explanations with examples, interactive tools, and visual demonstrations
Visit Math is Fun →Detailed tutorials on prime factorization methods with step-by-step examples
Visit Purplemath →Get all factors, prime factorization, and factor pairs in one calculation - more comprehensive than basic calculators.
See prime factorization in standard form (2³ × 3) and expanded form (2 × 2 × 2 × 3) for better understanding.
View all multiplication pairs that equal your number, useful for area problems and understanding relationships.
One-click access to common numbers (12, 24, 36, 100) for faster learning and testing.
12+ detailed FAQs covering factors, prime factorization, factor pairs, and real-world applications.
Learn division method, square root method, and prime factorization method with clear examples.
Clear side-by-side comparison helping students understand the difference between these related concepts.
Practical examples showing how factors are used in everyday life - from simplifying fractions to organizing groups.
Built-in reference table of common factor calculations for quick lookup and homework verification.
Visual method for finding prime factorization explained with step-by-step examples.
Lightning-fast calculations with immediate display of all factors, prime factors, and pairs.
No ads, no sign-up, no limitations. Completely free with unlimited calculations for everyone.