We can factorize each monomial as
[tex]9a^4b^6c^5=9a^4b^4b^2c^5[/tex]and
[tex]11a^4b^4c^7=11a^4b^4c^5c^2[/tex]To find the greastest common factor, we must take each monomial and write its prime fractorization. In our case, 11 is a prime number, so its factor are 1 and 11 only. So 1 is the common factor for 9 and 11.
Regarding to the variables, we can see that the greastest common factors are
[tex]a^4,b^4,c^5[/tex]Hence, the greatest common factor is
[tex]\begin{gathered} \text{GCF}=1\cdot a^4\cdot b^4\cdot c^5 \\ or \\ \text{GCF}=a^4\cdot b^4\cdot c^5 \end{gathered}[/tex]