Find integer factors, greatest common factors, and rational factors of quadratic trinomials.
02 · A little clarityEXAMPLE RESULT
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How 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. Choose the GCF mode to find the greatest common factor of a list of integers. For the smallest shared multiple, use the related LCM calculator.
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.
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