The given monomials are:
[tex]\begin{gathered} 28g^5h^2 \\ 12g^6h^5 \end{gathered}[/tex]
To find the greatest common factor, we need to write the prime factorization of each monomial and find the common factors:
[tex]\begin{gathered} 28g^5h^2=2*2*7*g*g*g*g*g*h*h \\ 12g^6h^5=2*2*3*g*g*g*g*g*g*h*h*h*h*h \end{gathered}[/tex]
They have two factors of 2, five factors of g and two factors of h in common.
The greatest common factor is the multiplication of these common factors, then it is:
[tex]\begin{gathered} GCF=2*2*g*g*g*g*g*h*h \\ GCF=4*g^5*h^2 \\ GCF=4g^5h^2 \end{gathered}[/tex]
The GCF is 4g^5h^2.
