1. **State the problem:** Factor the expression $$18m - 27n$$. 2. **Identify the greatest common factor (GCF):** The coefficients are 18 and 27. The GCF of 18 and 27 is 9. 3. **Apply the distributive property:** Factor out the GCF 9 from both terms: $$18m - 27n = 9(2m) - 9(3n) = 9(2m - 3n)$$ 4. **Check if further factoring is possible:** The expression inside the parentheses, $$2m - 3n$$, cannot be factored further because 2 and 3 have no common factors and the variables are different. 5. **Final factored form:** $$\boxed{9(2m - 3n)}$$ This is the fully factored form of the expression.