To find the factors of 81, we need to identify all the positive integers that divide 81 without leaving a remainder.
The prime factorization of 81 is: \[ 81 = 3^4 \]
Using the prime factorization, we can determine the factors: The factors of 81 are all the combinations of the prime factors raised to their respective powers:
- 3^0 = 1
- 3^1 = 3
- 3^2 = 9
- 3^3 = 27
- 3^4 = 81
So, the complete list of factors of 81 is: 1, 3, 9, 27, 81
Now, let's compare this with the options provided:
A (1, 9, 81) - Incomplete, missing 3 and 27. B (1, 3, 4, 9, 27, 81) - Incorrect, includes 4 which is not a factor of 81. C (1, 3, 9, 27, 81) - Correct, includes all the factors. D (1, 81) - Incomplete, missing 3, 9, and 27.
Therefore, the correct answer is C (1, 3, 9, 27, 81).