Factor Calculator
Find all factors of a whole number with factor pairs, prime factorization, factor count, proper factors, and number classification.
Last Updated: May 2026
Enter one nonzero integer. Negative inputs use the same positive factors as their absolute value.
Positive factors
1, 2, 3, 4, 6, 9, 12, 18, 36
Factor count
9
Prime factorization
2^2 x 3^2
Classification
Composite perfect square
| Property | Value |
|---|---|
| Input | 36 |
| Absolute value used | 36 |
| Prime factorization | 2^2 x 3^2 |
| Positive factors | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| Proper factors | 1, 2, 3, 4, 6, 9, 12, 18 |
| Sign note | Positive factor list shown. |
Each pair multiplies to the absolute value. Negative inputs also have matching negative-positive signed pairs.
Proper factors exclude the number itself. Their sum helps identify perfect, deficient, and abundant behavior.
Prime factorization gives a compact way to audit every divisor and count factors from exponent choices.
Factor Pairs
| Factor | Partner | Check |
|---|---|---|
| 1 | 36 | 1 x 36 = 36 |
| 2 | 18 | 2 x 18 = 36 |
| 3 | 12 | 3 x 12 = 36 |
| 4 | 9 | 4 x 9 = 36 |
| 6 | 6 | 6 x 6 = 36 |
Integer Factor Notice
This calculator is for integer factors and educational checking. Decimal inputs are not supported, and zero is excluded because it has infinitely many integer divisors.
Checked by Jitendra Kumar
Factor Calculator is checked for formula labels, source links, and result limits.
Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.
How to Use the Factor Calculator
Enter one nonzero whole number. The calculator accepts positive or negative integers up to an absolute value of 1,000,000,000,000.
Review the full factor list, factor pairs, prime factorization, factor count, and classification. Negative inputs use the same positive factors as their absolute value.
Step 1: Enter a whole number
Use one nonzero integer.
Step 2: Read the factor list
The highlighted result shows every positive factor.
Step 3: Check factor pairs
Use the pair table to verify each multiplication product.
Step 4: Review prime factorization
Use prime powers to audit the factor count and number type.
How This Factor Calculator Works
The calculator normalizes the input to its absolute value, finds the prime factorization by trial division, then builds every positive divisor from the prime powers.
Factor pairs are formed by pairing each divisor d with n / d. The table stops naturally when the first factor is larger than its partner.
The factor count comes from prime exponents. For example, if n = 2^2 x 3^2, the number of positive factors is (2 + 1)(2 + 1) = 9.
Factor Guide
Core Factor Rules
| Concept | Rule | Use |
|---|---|---|
| Factor definition | d divides n when n / d has no remainder | Identifies every divisor of the number. |
| Factor pair | a x b = n | Shows two factors that multiply to the original value. |
| Prime factorization | n = p1^a x p2^b x ... | Breaks the number into prime powers. |
| Factor count | (a + 1)(b + 1)... | Counts positive factors from prime exponents. |
| Proper factors | all positive factors except n | Used for perfect, abundant, and deficient checks. |
Factor Examples
| Input | Factors | Notes |
|---|---|---|
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 2^2 x 3^2 |
| 97 | 1, 97 | Prime number |
| 144 | 1 through factor pairs ending 12 x 12 | Perfect square |
| 28 | 1, 2, 4, 7, 14, 28 | Perfect number because proper factors sum to 28 |
Factor Context
Factors are the building blocks for divisibility tests, simplifying fractions, finding GCF and LCM, prime factorization, number classification, and many algebra and arithmetic workflows.
Keep the research moving with Modulo Calculator, GCF Calculator, LCM Calculator, and Integer Calculator.
Frequently Asked Questions
Related Calculators
Modulo Calculator
Calculate remainders, quotients, congruence checks, and divisibility.
Use Modulo CalculatorGCF Calculator
Calculate greatest common factors with Euclidean steps and prime factors.
Use GCF CalculatorLCM Calculator
Calculate least common multiples with pairwise steps and prime-power checks.
Use LCM CalculatorInteger Calculator
Calculate signed integer arithmetic, quotient and remainder, GCD, LCM, and powers.
Use Integer CalculatorRelated Guides
Factors, Multiples & Number Theory Guide
Use this for factors, multiples, GCF, LCM, prime numbers, prime factorization, divisibility tests, relatively prime numbers, digit sums, and digital roots.
Read guide
Math Formulae Page: 440 K-12 Formulas
Use this as a broad formula reference across arithmetic, algebra, geometry, trigonometry, statistics, matrices, vectors, and calculus readiness.
Read guideSources & References
- 1.Wolfram MathWorld - Divisor(Accessed May 2026)
- 2.Wolfram MathWorld - Prime Factorization(Accessed May 2026)
- 3.OpenStax Prealgebra - Factors and Multiples(Accessed May 2026)