Question

How do you find the GCF of `30w ^ { 4} ,42w ^ { 2},` and `12w`?

Answer 1

`6w`

Explanation:

Question: "What is the GCF of 30, 42, and 12?
Answer: 6

You may ask, "How did you get the answer?"
1) Let's list out the factors of 30, 42, and 12.

30 - 1, 2, 3, 5, 6, 10, 15, 30
42 - 1, 2, 3, 6, 7, 14, 21, 42
12 - 1, 2, 3, 4, 6, 12

What are the common numbers from the list?
1, 2, 3, 6

What is the greatest number from the list of the common numbers?
6

Now let's separate the variables and find the common factor of the variables.
Variables: `w^2`, `w^4`, `w`
*`w` can also be thought of as `w^1`.

Since `w` is the lowest powered variable and all of the other ones are greater than that. Then it means that the common factor of the variables is `w`.

Let's combine what we've found out now!
The GCF of the integers is 6 and the common factor of the variables is `w`. Therefore, the GCF is `6w`!