Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Luke Winspur*

Luke has taught high school algebra and geometry, college calculus, and has a master's degree in education.

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

The greatest common factor is usually used when simplifying fractions, and it's one of those topics that you learn pretty early on in your education but can easily forget or mistake for a different math idea, mainly the least common multiple. But before we can talk about the greatest common factor, often written as the GCF, we first have to know what a plain old regular factor is.

Simply put, the factors of a number are the smaller numbers that make up that original one. Saying that slightly more mathematically sounds like this: The factors of a number are the different numbers that you can multiply together to get that original number. But a lot of math topics are best shown with examples, and this is probably one of them.

Let's start by looking at the factors of 6. The factors of 6 are going to be 2 and 3, because 2 x 3 = 6. It's also true that 1 and 6 are factors, then, because 1 x 6 is also equal to 6. That gives us our full list for the factors of 6 as 1, 2, 3, and 6.

How about the factors of 60? Well, I know I can always do 1 times the number, so that works for this. Also, 60 is even, so I know 2 works, and 2 x 30 = 60. If we try dividing 60 by 3, we get 20, so that means I can add 3 and 20 to the list. If we continue on up, we find that 4 and 15, 5 and 12, 6 and 10 work - but the next one that works is 10 and 6, and this is basically just a repeat of 6 and 10. So, at this point we can stop, because the rest of the multiplication problems we do are just all repeats of numbers we've already got on our list. That makes the factors of 60 all the different numbers you see here: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Quite a lot of them.

So, now we're ready to talk about what this lesson is really on: **the greatest common factor**, or GCF. In order to find a GCF, we need to be looking at two numbers, say 10 and 22. Then, we simply ask ourselves, of the factors these two numbers have, which one's the biggest that they have in common?

Well, factors of 10 are 1 and 10 and 2 and 5, while the factors of 22 are 1 and 22 and 2 and 11. That makes the greatest common factor of 10 and 22 2, because it's the biggest number I see on both the lists. That's it!

Let's try a few more examples just to make sure you've got it. Maybe this one: find the GCF of 27 and 45. We'll start by listing out the factors of each of these numbers individually, just like we learned earlier.

Looking at 27 first, 1 will always work, so we can start there. 27 is odd, so 2 is not going to work, but we can do 3 x 9. The next one that works is 9 x 3, so you've started repeating, and we can stop. That makes our list for the factors for 27 pretty short - just 1, 3, 9 and 27.

Next with 45 - after we count 1 and 45, we can again rule 2 out, but 3 and 15 is good, 4 doesn't work, but 5 x 9 does, and the next one is 9 x 5, so we've hit our repeating point. That makes our list of factors of 45 what you see here: 1, 3, 5, 9, 15, 45.

So, answering the original question, 'What is the GCF of these two numbers?', is as easy as picking out the biggest number that is on both of these lists. Looks like 9 is our winner!

Last example: Find the greatest common factor between 4 and 16. We again begin by writing out all the factors of these two numbers. For 4, we get 1, 2 and 4, while for 16 we get 1, 2, 4, 8 and 16. So, the greatest common factor of 4 and 16 is the biggest number that's on both lists. That's 4.

Notice that 4 was one of the original numbers from the problem. That's totally okay! Some people get a little freaked out that this isn't allowed and decide to go with 2 instead because it's the next one down on the list. Don't do that! It's okay if the GCF is one of the original numbers from the problem.

To review: the factors of a number are the different numbers that you can multiply together to get that original number. The greatest common factor of two numbers is the biggest factor that they both have in common and is often written as the GCF for short. It's okay to have the GCF of two numbers be one of the original numbers itself. And finally, as a side note, the place in math where you'll use this the most often is when you're simplifying fractions.

Following this lesson, you'll be able to:

- Explain what the factors of a number are
- Describe how to find the greatest common factor of two numbers
- Identify when you will likely need to find the greatest common factor

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 1 of the course:

Back To Course

Math 102: College Mathematics15 chapters | 121 lessons | 13 flashcard sets

- GACE ESOL Test II: Practice & Study Guide
- GACE Science Test I: Practice & Study Guide
- GACE English Test II: Practice & Study Guide
- GACE ESOL Test I: Practice & Study Guide
- Computer Science 103: Computer Concepts & Applications
- Assessing Student Writing Skills
- Developing Student Vocabularies
- English Language Learners Instruction
- Understanding Computer Files
- Strategies for Developing Student Writing Skills
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- Chinese Cinderella: Characters & Quotes
- Local, National & Global Business: Definitions & Examples
- Cell Membrane Analogies
- Implications of Choice Theory on Social Policy & Crime
- The Greensboro Sit-In: Summary & Significance
- Scaffolding Strategies that Support Academic Language Proficiency
- Tarsier Monkey: Life Cycle & Reproduction
- Pig Farming Facts: Lesson for Kids
- Chemical Properties: Quiz & Worksheet for Kids
- Quiz & Worksheet - Endoplasmic Reticulum Facts for Kids
- Quiz & Worksheet - Indecent Exposure as a Legal Issue
- Quiz & Worksheet - Nucleolus Facts for Kids
- Boston Massacre Significance: Quiz & Worksheet for Kids
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- Frankenstein Study Guide
- Strategies for Competitive Advantage
- Basics of Accounting
- Mastering Effective Team Communication in the Workplace
- PLACE English: Practice & Study Guide
- Communication in Relationships
- NMTA Essential Academic Skills Math: Data & Statistics
- Quiz & Worksheet - Organic Chemical Reactions
- Quiz & Worksheet - The Common Application
- Quiz & Worksheet - Find Colleges with Good Career and Salary Prospects
- Quiz & Worksheet - Lymph Nodes Anatomy
- Quiz & Worksheet - Crystalloids

- How To Evaluate College Admissions Criteria
- Who Was Leif Erikson? - Facts and Biography
- What's the AP Exam Schedule?
- Creative Writing Lesson Plan
- PSAT Tips & Tricks
- Black History Month for Kids
- How to Use the GED Math Prep Course
- Debate Lesson Plan
- How Long is the PSAT Test?
- Water Cycle for Kids: Activities & Games
- Illinois TAP Test Pass Rate
- 3rd Grade Science Projects

Browse by subject