1. **State the problem:** Find the greatest common factor (GCF) of 18 and 36b. 2. **Recall the formula and rules:** The GCF of two expressions is the largest expression that divides both without remainder. 3. **Factor each term:** - 18 factors as $2 \times 3^2$ - 36b factors as $2^2 \times 3^2 \times b$ 4. **Find common factors:** - Common prime factors are $2$ and $3^2$ - The smallest power of 2 common to both is $2^1$ - The smallest power of 3 common to both is $3^2$ - Variable $b$ is only in 36b, so it is not common 5. **Calculate GCF:** $$\text{GCF} = 2^1 \times 3^2 = 2 \times 9 = 18$$ 6. **Answer:** The greatest common factor of 18 and 36b is $18$.