Quick answer
A factor of n is a whole number that divides it with no remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 (nine factors), and 36 = 2² × 3².
Enter a whole number up to 10¹². The calculator lists its factors and counts them.
Related tools: Common Factor Calculator: All common factors of two numbers. Power Factor Calculator: Power factor, phase angle and reactive power from real and apparent power. Slope Calculator: Slope, angle, distance and line equation through two points.
How to use the Factor Calculator
- Enter number (a whole number, between 1 and 1000000000000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A whole number | ≥ 1, ≤ 1000000000000 |
Formula and method
Formula
d is a factor of n when n mod d = 0
IEEE-754 double precision; shown to at most 6 decimal places.
Trial division up to √n; each divisor d pairs with n ÷ d.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 36.
| Result | Value |
|---|---|
| Factors | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| Number of factors | 9 |
Example 2
Inputs: Number = 1.
| Result | Value |
|---|---|
| Factors | 1 |
| Number of factors | 1 |
Example 3
Inputs: Number = 97.
| Result | Value |
|---|---|
| Factors | 1, 97 |
| Number of factors | 2 |
The first line is the headline result (factors). Below it the factor Calculator lists number of factors, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Counting factors from the prime factorisation
If n = p^a × q^b, the number of factors is (a + 1)(b + 1). For 36 = 2² × 3², that is 3 × 3 = 9. Perfect squares always have an odd number of factors because one factor pairs with itself (6 × 6).
Factor pairs
Pair each factor with its partner: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. A prime has just two factors, 1 and itself, and 1 has only itself.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Factors | Number of factors |
|---|---|---|
| 18 | 1, 2, 3, 6, 9, 18 | 6 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 9 |
| 72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 | 12 |
| 144 | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | 15 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: entering "0" shows "Number must be at least 1." beside that field and no result.
Choosing between the Factor Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Common Factor Calculator](/math/common-factor-calculator/) | first number and second number | Common factors |
| [Power Factor Calculator](/math/power-factor-calculator/) | real power and apparent power | Power factor |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Quadratic Formula Calculator](/math/quadratic-formula-calculator/) | a, b and c | Roots |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- 1 has only itself as a factor
- Maximum 10^12
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number to confirm this.
Frequently asked questions
What are the factors of 12?
1, 2, 3, 4, 6 and 12.
Is 0 a factor?
No; factors of a positive number are positive divisors.
What is the difference between factors and multiples?
Factors divide the number; multiples are the number times a whole number.
What does the Factor Calculator calculate?
List every factor of a positive whole number. It returns Factors and Number of factors.
What formula does the Factor Calculator use?
d is a factor of n when n mod d = 0. Trial division up to √n; each divisor d pairs with n ÷ d.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. 1 has only itself as a factor.
What are the limits of this calculator?
1 has only itself as a factor. Maximum 10^12.
What is an example of a factor result?
With number 36, the factors is 1, 2, 3, 4, 6, 9, 12, 18, 36.
Related calculators
- Common Factor Calculator — All common factors of two numbers.
- Power Factor Calculator — Power factor, phase angle and reactive power from real and apparent power.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
- Log Calculator — Logarithm of a number to any base.
- Exponential Decay Calculator — Exponential decay over time at a constant percentage rate.
- Polynomial Calculator — Add, subtract or multiply two polynomials, and evaluate the result.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.