Find the greatest common factor of these three expressions. $30 v^{4}, 18 v^{5}$, and $12 v$

Step 1 ：Given the expressions $30 v^{4}, 18 v^{5}$, and $12 v$, we need to find the greatest common factor (GCF).

Step 2 ：The GCF of a set of numbers is the largest number that divides evenly into each of the numbers. It can be found by listing the prime factors of each number, and then multiplying the common factors.

Step 3 ：For the given expressions, we need to find the GCF of the coefficients and the powers of v separately.

Step 4 ：The coefficients are 30, 18, and 12. The GCF of these numbers is 6.

Step 5 ：The powers of v are 4, 5, and 1. The GCF of the powers is the smallest power, which is 1.

Step 6 ：Therefore, the GCF of the given expressions is $6v^{1}$ or simply $6v$.

Step 7 ：\(\boxed{6v}\) is the greatest common factor of the expressions $30 v^{4}, 18 v^{5}$, and $12 v$.