Factor Calculator

Factor one whole number, or a quadratic with whole-number coefficients.

Smart Tips

• Positive factors are listed for the absolute value. A negative number keeps a −1 in the prime factorization.

• 1 has no prime factors. 0 is rejected, because every nonzero integer divides 0.

• The integer cap is ±1,000,000,000,000 so trial division finishes at once. Larger values are rejected.

• A quadratic is factored only when the factors have whole-number coefficients. There is no cubic solver.

The Formula

n = p₁^a₁ × p₂^a₂ × … ax² + bx + c = g(px + q)(rx + s)

n The integer
Trial division up to √|n|

p Prime factors
Ladder method, smallest prime first

g Greatest common factor
Pulled out of the quadratic first

D Discriminant
b² − 4ac, shown with the factorization

Integer pairs are tried after the common factor is removed. If no pair multiplies to a and adds to b, the trinomial does not factor over the integers.

Key Insights

A hard cap

Anything outside ±1,000,000,000,000 is rejected. A prime near that cap still returns in a fraction of a second.

Perfect squares

When a factor repeats in a pair, the page says the integer is a perfect square.

Equal binomials

x² − 6x + 9 is written (x − 3)², not as two copies of the same binomial.

Not a cubic

Degree 3 and the quadratic formula live on other tools. This page stops at integer factors.

Frequently Asked Questions

Every positive factor of the absolute value, and the prime factorization. Negatives are written with a leading −1. 1 has no prime factors. 0 is rejected.

Trial division stops at the square root. The page accepts whole numbers from −1,000,000,000,000 through 1,000,000,000,000 so the search returns immediately. Larger integers are rejected. Quadratic coefficients stop at ±1,000,000.

The page says it does not factor over the integers and still shows the discriminant. That is a result, not an error. There is no degree-3 solver.

An integer whose prime exponents are all even is marked as a perfect square. A repeated binomial such as (x − 3)(x − 3) is written (x − 3)².

Yes, within ±1,000,000. The written factors prefer a positive leading coefficient when that choice is available. The coefficient of x² cannot be 0, because that would be a linear expression.

Prime factorization follows the ladder method in OpenStax Prealgebra 2e, section 2.5, Prime Factorization and the Least Common Multiple. Quadratics follow the trial-and-error method in OpenStax Intermediate Algebra 2e, section 6.2, Factor Trinomials.

Responsive Ad Space

Prime factorization

Enter values to calculate

Positive factors

Perfect square

Note:Integers are capped at ±1,000,000,000,000 and quadratic coefficients at ±1,000,000 so the search returns immediately. A trinomial that does not factor over the integers is a result, not an error. This is not a cubic solver.