Polynomial GCD Calculator
Enter the coefficients of two polynomials to find their greatest common divisor.
Result
How to use
- Enter your values in the fields above.
- Press Calculate to see your result instantly.
- Use the Share button to copy a link to your result.
About this calculator
Just as integers have a greatest common divisor, two polynomials have a polynomial GCD — the highest-degree polynomial that divides both of them with no remainder. It's computed with the same Euclidean algorithm used for integers: repeatedly take the remainder of dividing the higher-degree polynomial by the lower-degree one until the remainder is zero, then normalize the result to monic form (leading coefficient 1) for a unique answer.
Polynomial GCD is a building block in computer algebra systems (Mathematica, Maple, SymPy) for simplifying rational expressions and factoring, and it underlies decoding algorithms for Reed-Solomon error-correcting codes used in QR codes, CDs, and satellite communication.
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