1. **State the problem:** We have Set A as the positive factors of 81 and Set B as the positive multiples of 9. We need to find Set C, which is the intersection of Sets A and B, meaning all elements common to both sets. 2. **Find Set A:** The positive factors of 81 are numbers that divide 81 without remainder. Since $81 = 3^4$, its positive factors are: $$1, 3, 9, 27, 81$$ 3. **Find Set B:** The positive multiples of 9 are numbers like: $$9, 18, 27, 36, 45, 54, 63, 72, 81, \ldots$$ 4. **Find the intersection Set C:** We look for numbers that are both factors of 81 and multiples of 9. From Set A and Set B: - Factors of 81: $\{1, 3, 9, 27, 81\}$ - Multiples of 9: $\{9, 18, 27, 36, 45, 54, 63, 72, 81, \ldots\}$ Common elements are $9, 27, 81$. 5. **Answer:** Set C = $\{9, 27, 81\}$. Therefore, the correct choice is **E 9, 27, 81**.