# How to Find the Greatest Common Factor (GCF)? (+FREE Worksheet!)

The Greatest Common Factor (GCF), as its name implies, is the greatest number between the common factors of two numbers. In this post, you learn how to find the Greatest Common Factor (GCF) of two or more numbers using a few simple and easy steps.

Common factors of numbers are factors that are common to both numbers. The Greatest Common Factor (GCF), as its name implies, is the greatest number between the common factors of two numbers. One of the most important uses of the Greatest Common Factor (GCF) is to simplify fractions.

**The Absolute Best Books to Ace Pre-Algebra to Algebra II**

## Related Topics

## A step-by-step guide to finding the Greatest Common Factor

There are two ways to calculate the largest common factor:

**1- Use a list of factors to find the Greatest Common Factor (GCF)**

**Step 1:**To find the largest common factor between a set of numbers, list all the factors in each number.**Step 2:**Next, select the common factors.**Step 3:**Finally, the greatest factor in all lists is The Greatest Common Factor (GCF).

**2- Use the prime factorization to find the Greatest Common Factor (GCF)**

You can use prime factorization to find the Greatest Common Factor (GCF) for a set of numbers. In the case of bigger numbers – which are time-consuming to create a list of factors – this method usually works best.

**Step 1:**List the prime factors of each number.**Step 2:**Draw a circle around the prime factors that are common to all lists.**Step 3:**Multiply the numbers which you have drawn a circle around them. The answer is the Greatest Common Factor (GCF) between those numbers.

**Note:**If there are no common prime factors, the**GCF (Greatest Common Factor)**is \(1\).

### Greatest Common Factor – Example 1:

Find the **GCF **for \(8\) and \(12\).

**Solution:**

The factors of \(8\) are: \( \{1, 2, 4, 8\} \)

The factors of \(12\) are: \( \{1,2,3,4,6,12\} \)

Numbers \(2\) and \(4\) are in common.

Then the greatest common factor is: \(4\).

### Greatest Common Factor – Example 2:

Find the **GCF **for \(14\) and \(18\).

**Solution:**

The factors of \(14\) are: \( \{1,2,7,14\} \)

The factors of \(18\) are: \( \{1,2,3,6,9,18\} \)

There is \(2\) in common

Then the greatest common factor is: \(2\).

** The Best Book to Help You Ace**** Pre-Algebra**

### Greatest Common Factor – Example 3:

Find the **GCF **for \(10\) and \(15\) and \(25\) .

**Solution:**

The factors of \(10\) are: \(\{1,2,5,10\}\)

The factors of \(15\) are: \(\{1,3,5,15\}\)

The factors of \(25\) are: \(\{1,5,25\}\)

Factor \(5\) is in common.

Then the greatest common factor is: \(5\).

### Greatest Common Factor – Example 4:

Find the **GCF **for \(8\) and \(20\).

**Solution:**

The factors of \(8\) are: \(\{1,2,4,8\}\)

The factors of \(20\) are: \(\{1,2,4,5,10,20\}\)

Numbers \(2\) and \(4\) are in common.

Then the greatest common factor is: \(4\).

## Exercises for practicing the Greatest Common Factor

### Find the **GCF** for each number pair.

- \(\color{blue}{20, 30}\)
- \(\color{blue}{4, 14}\)
- \(\color{blue}{5, 45}\)
- \(\color{blue}{68, 12}\)
- \(\color{blue}{5, 6, 12}\)
- \(\color{blue}{15, 27, 33}\)

### Download Greatest Common Factor Worksheet

- \(\color{blue}{10}\)
- \(\color{blue}{2}\)
- \(\color{blue}{5}\)
- \(\color{blue}{4}\)
- \(\color{blue}{1}\)
- \(\color{blue}{3}\)

**The Greatest Books for Students** **to Ace the Algebra**

## Related to This Article

### More math articles

- How to Prepare for the CLEP College Algebra Test?
- Top 10 PSAT/NMSQT Math Practice Questions
- What Kind of Math Is on the Praxis Core Test?
- FREE ISEE Middle Level Math Practice Test
- 10 Most Common 5th Grade IAR Math Questions
- FREE 3rd Grade SBAC Math Practice Test
- The Ultimate ASVAB Math Course (+FREE Worksheets & Tests)
- How to Solve Rational Numbers Word Problems
- 4th Grade PSSA Math Worksheets: FREE & Printable
- Number Properties Puzzle -Critical Thinking 2

## What people say about "How to Find the Greatest Common Factor (GCF)? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.