## What is a Greatest Common Factor?

The Greatest Common Factor (GCF) is the largest number or polynomial that can divide evenly into a set of numbers or terms. In this case, we will be finding the GCF of the expressions 2x^3y, x^2y^2, and 4xy^3.

## Step-by-Step Process to Find the GCF

- Step 1: Identify the prime factors of each term
- 2x^3y = 2 * x * x * x * y
- x^2y^2 = x * x * y * y
- 4xy^3 = 2 * 2 * x * y * y * y
- Step 2: Determine the common factors and their highest powers
- The common factors are 2, x, and y.
- The highest power of 2 is 2.
- The highest power of x is 1.
- The highest power of y is 1.
- Step 3: Multiply the common factors with their highest powers
- GCF = 2 * x * y = 2xy

To find the GCF, we need to break down each term into its prime factors. Let’s break down the expressions:

Next, we identify the common factors across all the expressions and their highest powers:

To find the GCF, we multiply the common factors with their highest powers identified in the previous step:

## The Greatest Common Factor of 2x^3y, x^2y^2, and 4xy^3 is 2xy.

Remember, the GCF represents the largest term that can divide evenly into all of the given expressions. In this case, 2xy can be factored out from each term without leaving any remainder.

By finding the GCF, we can simplify expressions, factor polynomials, and solve equations more efficiently. It is an essential concept in algebra and helps us work with expressions in a more manageable form.

Practice finding the GCF of different expressions to improve your algebra skills and problem-solving abilities.

Now that you understand how to find the GCF of 2x^3y, x^2y^2, and 4xy^3, you can apply this method to other similar problems.