Factor Calculator
List every factor of a number and identify whether it's prime.
About Factor Calculator
A factor (or divisor) of an integer n is a number that divides n exactly, leaving no remainder. Every positive integer has at least two factors: 1 and itself. A prime number has exactly those two — no others. The factor pairs of n are all (a, b) with a ≤ b and a × b = n. This calculator finds factors by trial division from 1 to √n, which is efficient for numbers up to ~10⁹.
Formulas
Factor condition
d divides n if and only if n mod d = 0
Factor count bound
Factors come in pairs (d, n/d), so total factors ≤ 2√n
Worked example
With the default values below, Factor Calculator returns Number of Factors of 9. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numberaccepts 1–1,000,000,000
- 36
Results
- Number of Factors
- 9
- Factors
- 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factor Pairs
- 1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6
- Is Prime?
- No — composite (9 factors)
Step by step
- 1Number= 36
- 2Factors (9)= 1, 2, 3, 4, 6, 9, 12, 18, 36
- 3Factor pairs= 1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6
- 4Prime?= No
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What makes a number prime?
A prime number has exactly two distinct factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13. Note that 1 is not prime (it has only one factor), and 2 is the only even prime.
What is the difference between factors and multiples?
Factors divide evenly into n. Multiples are n multiplied by positive integers. The factors of 12 are 1, 2, 3, 4, 6, 12. The multiples of 12 are 12, 24, 36, 48, …
How many factors does 36 have?
36 = 2² × 3². Using the formula for the number of factors: (2+1)(2+1) = 9. The factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.