To find the Highest Common Factor of $18x$ and $27x^2$,
$18x=2\times$
$\times$
$27x^2=3\times$
$\times$
$\times$
$18x=2\times \textcolor{red}{9} \times \textcolor{red}{x}$
$27x^2= 3\times \textcolor{red}{9} \times \textcolor{red}{x} \times x$
The HCF is $\textcolor{red}{9} \times \textcolor{red}{x}=$
To find the Highest Common Factor of $2x^3$ and $x^2\left(x+1\right)$,
$2x^3=2\times$
$\times$
$\times$
$x^2 \left(x+1\right)=$
$\times$
$\times$
$2x^3=2\times \textcolor{red}{x} \times \textcolor{red}{x} \times x$
$x^2 \left(x+1\right)= \textcolor{red}{x} \times \textcolor{red}{x} \times \left(x+1\right)$
The HCF is $\textcolor{red}{x} \times \textcolor{red}{x}=$
To find the Highest Common Factor of $6\left(x+3\right)\left(x-2\right)$ and $8\left(x+3\right)^2$,
$6\left(x+3\right)\left(x-2\right)= \textcolor{red}{2} \times$
$\times$
$\times \left(x-2\right)$
$8\left(x+3\right)^2= \textcolor{red}{2} \times$
$\times$
$\times$
$6\left(x+3\right)\left(x-2\right)= \textcolor{red}{2}\times 3\times \textcolor{red}{x+3} \times \left(x-2\right)$
$8\left(x+3\right)^2= \textcolor{red}{2} \times 4\times \textcolor{red}{x+3} \times \left(x+3\right)$
The HCF is $\textcolor{red}{2} \times \textcolor{red}{x+3}=$