Since contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

Steps to find the GCF for :

1. Find the GCF for the numerical part

2. Find the GCF for the variable part

3. Multiply the values together

Find the common factors for the numerical part:

The factors for are all numbers between and , which divide evenly.

Check numbers between and

Find the factor pairs of where .

List the factors for .

The factors for are all numbers between and , which divide evenly.

Check numbers between and

Find the factor pairs of where .

List the factors for .

The factors for are all numbers between and , which divide evenly.

Check numbers between and

Find the factor pairs of where .

List the factors for .

List all the factors for to find the common factors.

:

:

:

The common factors for are .

The GCF for the numerical part is .

Next, find the common factors for the variable part:

The factors for are .

The factors for are .

The factors for are .

The factors for are .

The factor for is itself.

x

The factors for are .

List all the factors for to find the common factors.

The common factors for the variables are .

The GCF for the variable part is .

Multiply the GCF of the numerical part and the GCF of the variable part .

Find the GCF 2x^4y^2+8x^2y^3+4xy^4