### Theory:

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 $$(HCF)$$.
Example:
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:
1. Resolve each polynomials or expressions into factors.
2. The product of common factors with highest degree will be the $$GCD$$ of the polynomial.
3. 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.
4. Prefix the $$GCD$$ of the numerical part as a coefficient to the $$GCD$$ of the polynomial.