To find the greatest common factor (GCF) of the expressions \( 18y18y \) and \( 18x18x \), we first rewrite these expressions more clearly:
- The expression \( 18y18y \) can be interpreted as \( 18y^2 \) (since \( y18y \) seems to be a typographical error).
- The expression \( 18x18x \) can similarly be interpreted as \( 18x^2 \) (for the same reason).
Now, we have two expressions: \( 18y^2 \) and \( 18x^2 \).
Next, we identify the common factors.
- The numerical part \( 18 \) is common in both expressions.
- The variable terms \( y^2 \) and \( x^2 \) do not have any common factors since they involve different variables.
Thus, the GCF is based solely on the numerical coefficient:
\[ \text{GCF}(18y^2, 18x^2) = 18 \]
Therefore, the greatest common factor of \( 18y^2 \) and \( 18x^2 \) is \( \boxed{18} \).