1. **State the problem:** Find the factors of 81. 2. **Definition:** Factors of a number are integers that divide the number exactly without leaving a remainder. 3. **Method:** To find factors, check all integers from 1 up to 81 and see which divide 81 evenly. 4. **Prime factorization:** First, find the prime factors of 81. $$81 = 3^4$$ 5. **Generate factors:** Factors are all numbers of the form $$3^k$$ where $$k = 0,1,2,3,4$$ multiplied by any other factors (in this case, only 1). 6. **List factors:** - $$3^0 = 1$$ - $$3^1 = 3$$ - $$3^2 = 9$$ - $$3^3 = 27$$ - $$3^4 = 81$$ 7. **Final answer:** The factors of 81 are $$1, 3, 9, 27, 81$$.