Factors of $25$ are:

Given number is $25.$

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,

$$\begin{gathered} 1 \times 5 = 25, \\ 5 \times 5 = 25, \\ 25\times 1=25 \end{gathered}$$

There is no remainder when $25$ is divided by either $1, 5 \mathrm{or} 25$.

Therefore, the factors of $25$ are $1, 5 \mathrm{and} 25$.

Hence, the correct answer is option D.