The Highest Common Factor (HCF) of two or more given polynomials is the product of the polynomials of highest degree and greatest numerical coefficient each of which is a factor of each of the given polynomials.
The HCF of monomials is found by multiplying the HCF of numerical coefficients of each of the monomials and the variables with highest powers common to all the monomials.
For example, the HCF of monomials 12x2y3, 18xy4 and 24x3y5 is 6xy3 since HCF of 12, 18 and 24 is 6 and the highest powers of variable factors common to the polynomials are x and y3.
To determine the HCF of polynomials, which can be easily factorized, you express each of the polynomials as the product of the factors. Then the HCF of the given polynomials is the product of the HCF of numerical coefficients of each of the polynomials and factors with highest powers common to all the polynomials.