Factor Calculator
Every factor and factor pair of a whole number.
Inputs
Use this calculator on your own site
Free embed
- Two lines of HTML, unlimited views
- Shows a small CalculateEveryday bar, with a credit link under the calculator
Formula
Divide n by 1, 2, 3 … up to √n; every divisor that leaves no remainder gives a pair (d, n ÷ d)
A factor of n divides it exactly. Factors come in pairs that multiply to n, and one of each pair is never larger than √n — so testing divisors up to the square root finds them all. A number with exactly two factors, 1 and itself, is prime; more than two makes it composite.
Worked example
Testing 1 through 6 (the square root of 36) finds the pairs 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. That is nine factors — 1, 2, 3, 4, 6, 9, 12, 18, 36 — adding to 91. An odd count of factors always means a perfect square.
Where this can give the wrong answer
- This finds the factors of a whole number. Factoring an algebraic expression such as x² + 5x + 6 is a different problem — the quadratic calculator gives the roots that factoring would.
- 1 has a single factor and is neither prime nor composite, by definition.
- Negative factors are left out. Every pair also works with both signs flipped (−4 × −9 = 36), but listing them doubles the table without adding information.
- Numbers up to one trillion are supported; beyond that, whole numbers stop being exactly representable in the browser.
FAQ
- Factors are every whole number that divides n: for 36 there are nine. Prime factors are the primes that multiply to make it: 36 = 2 × 2 × 3 × 3. The prime factorization calculator gives that breakdown.
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