CalcCommonsHow to use
Choose integer factors, GCF, or quadratic factoring. Enter a single positive integer, a list of integers, or the coefficients a, b, and c of ax² + bx + c. Quadratic mode explicitly identifies cases outside rational factorization.
For related tasks, try the Long Division Calculator.
Formula & how it works
An integer factor divides n with zero remainder. GCF uses Euclid’s remainder algorithm. Quadratic roots are (−b ± √(b² − 4ac))/(2a); rational roots give a(x − r₁)(x − r₂).
Worked example
Example 1
84 = 2 × 2 × 3 × 7. The GCF of 24, 36, and 60 is 12. For x² − 5x + 6, the discriminant is 1 and the factors are (x − 3)(x − 2).
Assumptions & practical notes
This is not a symbolic algebra system. Quadratic coefficients must be integers between −10,000 and 10,000, with a nonzero a.
Quadratics with irrational or complex roots are identified as outside the rational factor mode. Integer factorization is bounded at 1 billion.
See our calculation methodology for unit definitions and testing practices.
Frequently asked questions
Is 1 prime?
No. It has a single positive factor, 1, and no prime factors.
Can I enter an arbitrary expression?
No. Enter the three coefficients of a quadratic, or choose the integer/GCF modes.
Related calculators
Long Division Calculator
Divide nonnegative whole numbers with a quotient, remainder, and generated division steps.
Fraction Calculator
Add, subtract, multiply, divide, and convert fractions, mixed numbers, and decimals.
Right Triangle Calculator
Solve a right triangle from two sides or one side and an acute angle.