Greatest common divisor:
The greatest common factor (\(GCD)\) of two or more polynomial is a polynomial of highest degree common to both the polynomials. In other words, the common factor of the polynomials with the highest degree. It is also called the Highest Common Factor \((HCF)\).
Consider the polynomials \(12xyz\) and \(3x\).
Here the coefficients \(12\) and \(3\) have the only highest common divisor \(3\).
Thus, the \(GCD\) of the numerical part is \(3\).
Also, the variables \(xyz\) and \(x\) have \(x\) as the only common divisor with highest degree.
Hence, the \(GCD\) of the variable part is \(x\).
Therefore, the \(GCD\) of the polynomials \(12xyz\) and \(3x\) is \(3x\).
Procedure to find the \(GCD\) by factorisation:
- Resolve each polynomials or expressions into factors.
- The product of common factors with highest degree will be the \(GCD\) of the polynomial.
- If the polynomials consists if numerical part, then the highest divisor common to both the coefficient part of the polynomials will be the \(GCD\) of the numerical part.
- Prefix the \(GCD\) of the numerical part as a coefficient to the \(GCD\) of the polynomial.