To determine what factor of 162 is a perfect fourth, we first need to understand what a perfect fourth is. A perfect fourth is a number that can be expressed as the fourth power of an integer. For example, 14 = 1, 24 = 16, and 34 = 81.
Next, we need to find the factors of 162. The factors of 162 are the numbers that can evenly divide it without leaving a remainder. The complete list of factors for 162 is: 1, 2, 3, 6, 9, 18, 27, 54, and 81.
Now, we check which of these factors are perfect fourths. Looking at the list:
- 1 is a perfect fourth (14 = 1).
- 2, 3, 6, 9, 18, 27, and 54 are not perfect fourths.
- 81 is also not a perfect fourth since it can be expressed as 34 = 81.
Therefore, the only factor of 162 that is a perfect fourth is 1.