# Precalculus Examples

Step 1

Since contains 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

Step 2

Find the common factors for the numerical part:

Step 3

Step 3.1

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

Check numbers between and

Step 3.2

Find the factor pairs of where .

Step 3.3

List the factors for .

Step 4

Step 4.1

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

Check numbers between and

Step 4.2

Find the factor pairs of where .

Step 4.3

List the factors for .

Step 5

Step 5.1

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

Check numbers between and

Step 5.2

Find the factor pairs of where .

Step 5.3

List the factors for .

Step 6

List all the factors for to find the common factors.

:

:

:

Step 7

The common factors for are .

Step 8

The GCF for the numerical part is .

Step 9

Next, find the common factors for the variable part:

Step 10

The factors for are .

Step 11

The factors for are .

Step 12

The factor for is itself.

Step 13

The factor for is itself.

Step 14

List all the factors for to find the common factors.

Step 15

The common factor for the variables is .

Step 16

The GCF for the variable part is .

Step 17

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