About Factor Pairs Calculator
This factor pairs calculator lists every pair of whole numbers that multiply to the number you enter, together with its full list of factors and its prime factorization. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 36, which has 9 factors and five pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. A number has an odd count of factors exactly when it is a perfect square, because the middle pair repeats the same number.
The list comes from the prime factorization, so it is exact even for numbers with many digits.
How to use Factor Pairs Calculator
- Pick Polynomial or Whole number.
- For a polynomial, type it using ^ for powers, for example x^3 + x^2 + 2x + 2, or use the keypad.
- Read the factored form at the top. It updates as you type.
- Open the steps to see each method applied, and the expansion check underneath.
- For a whole number, read the factor pairs, the full list of factors and the prime factorization.
Features
- Greatest common factor taken out first, including numbers and powers of x.
- Difference of squares, sum of cubes and difference of cubes recognised by pattern.
- Perfect square trinomials and general trinomials through the rational root theorem.
- Factoring by grouping for four-term polynomials.
- Repeated application, so x⁴ - 16 splits into (x - 2)(x + 2)(x² + 4).
- An expansion check that multiplies the factors back out.
- Whole-number mode with factor pairs, all factors and the prime factorization.
- Math keypad and live preview, usable on a phone.
How many factors
Write the number as a product of prime powers and add one to each exponent, then multiply.
36 = 2² × 3²
factors = (2 + 1)(2 + 1) = 9Worked examples
Factor pairs of 36 gives 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Nine factors in all.
Factor pairs of 97 gives 1 × 97
97 is prime, so it has only one pair.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The expressions you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Always take out the greatest common factor first. It often turns a hard trinomial into an easy one.
- Multiply your factors back out to check them. The calculator does this for you under the steps.
- If a quadratic is irreducible over the rationals, its discriminant is not a perfect square. Try the quadratic formula calculator for its exact roots.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Expressions are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Expressions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What are the factor pairs of 36?
1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
Why do perfect squares have an odd number of factors?
Factors come in pairs, except when the pair is the same number twice, like 6 × 6. That single factor makes the count odd.
More Factoring Calculator pages
- Factoring CalculatorType a polynomial to factor it with every step, or switch to a whole number for its factor pairs.
- Factor Trinomials CalculatorType a trinomial and get its two factors with the working.
- Difference of Squares CalculatorType an expression like 4x² - 25 and see it factored as a difference of squares.
- Sum and Difference of Cubes CalculatorType a cubic like 27x³ + 8 and see it factored with the cube formulas.
- Factor by Grouping CalculatorType a four-term polynomial and see it factored by grouping.
- Perfect Square Trinomial CalculatorType a trinomial and see whether it is a perfect square.
- GCF of a Polynomial CalculatorType a polynomial and see its greatest common factor taken out.