To factor the expression \(18r - 45s\), we first find the greatest common factor (GCF) of the coefficients 18 and 45.
The factors of 18 are: \(1, 2, 3, 6, 9, 18\)
The factors of 45 are: \(1, 3, 5, 9, 15, 45\)
The GCF of 18 and 45 is \(9\).
Now we can factor out the GCF from the expression:
\[ 18r - 45s = 9(2r - 5s) \]
Thus, the expression \(18r - 45s\) can be written as:
\[ \boxed{9(2r - 5s)} \]