Factors of $9$ are:

Given number is $9$.

We have to find the factors of the given number.

A number is said to be a factor of any other number, if it divides the second number completely without leaving any remainder.

Here, 

$$\begin{gathered} 1 \times 9 = 9, \\ 3 \times 3 = 9, \\ 9 \times 1 = 9 \end{gathered}$$

There is no remainder when $9$ is divided by either $1, 3 \mathrm{or} 9.$

Therefore, the factors of $9$ are $1, 3 \mathrm{and} 9.$

Hence, the correct answer is option C.