Find the greatest common factor (GCF) of $30 x$ and $25 x^{3}$.

Step 1 ：Given two monomials, $30x$ and $25x^{3}$, we are asked to find the greatest common factor (GCF).

Step 2 ：The GCF of two monomials is found by finding the GCF of their numerical coefficients and the least power of their common variables.

Step 3 ：The numerical coefficients are 30 and 25. The common variable is $x$ with powers 1 and 3 respectively.

Step 4 ：First, we find the GCF of 30 and 25. The GCF of 30 and 25 is 5.

Step 5 ：Next, we find the least power of $x$. The least power of $x$ is 1.

Step 6 ：Therefore, the GCF of $30x$ and $25x^{3}$ is $5x^{1}$ or simply $5x$.

Step 7 ：\(\boxed{5x}\) is the greatest common factor (GCF) of $30x$ and $25x^{3}$.