For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

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## Table of Contents

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### Greatest Common Factor

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- Factor: A part of a number that can be divided out without leaving a remainder
- Greatest Common Factor (GCF): the largest factor that divides two numbers

### Greatest Common Factor

- 9 ×1 = 9, 9 ×3 = 27

- 8 ×1 = 8, 8 ×3 = 24

- 6 ×4 = 24, 6 ×3 = 18

- 8 ×9 = 72, 8 ×8 = 64

- 5 ×3 = 15, 5 ×9 = 45
- 3 ×1 = 3, 3 ×3 = 9
- 5 ×3

- 18 ×1 = 18,18 ×2 = 36

- 14 ×1 = 14, 14 ×2 = 28

- 6 ×2 = 12, 6 ×5 = 30

- 6 ×9 = 54, 6 ×8 = 48

- 7 ×7 = 49, 7 ×8 = 56

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Greatest Common Factor

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Terms to Review 0:05
- Factor
- Example: Factor of 20
- Two Methods 0:59
- Greatest Common Factor
- Method 1: GCF of 15 and 30
- Method 2: GCF of 15 and 30
- Extra Example 1: Find the GCF of 6 and 18 5:16
- Extra Example 2: Find the GCF of 36 and 27 7:43
- Extra Example 3: Find the GCF of 6 and 18 9:18
- Extra Example 4: Find the GCF of 54 and 36 10:30

### Basic Math Online Course

### Transcription: Greatest Common Factor

*Welcome back; this lesson is on the greatest common factor.*0000

*Let's go over what a factor is.*0008

*A factor is a part of a number that can be divided out without leaving a remainder.*0011

*If we have the number 20, it is all the parts of 20 that can be multiplied into 20 without leaving a remainder.*0018

*An example of 20, factors would be 1... we know that 1 can be multiplied to get 20.*0030

*2 is a factor of 20; 4, 5, 10, and the number itself 20.*0038

*These are all considered to be factors of 20.*0052

*When we think of greatest common factor, we know that we have to find a common factor.*0062

*That means we are comparing two different numbers.*0070

*We have to find the biggest factor between the two numbers.*0073

*We can also call greatest common factor, GCF; it is also known as GCF.*0078

*If you look at this example right here between 15 and 30,*0084

*we are going to use these two numbers, compare them,*0088

*and find the factor that is the biggest between them.*0090

*There is two methods to solve this; the first method is very simple.*0095

*All you need to do is list out the factors.*0099

*15, I know the factors of 15 would be 1, 3, 5, and 15.*0107

*For 30, the factors are 1, 2, 5, 6, 10... I forgot 3... and 30 itself.*0118

*If I look at these... I have one more, 15.*0138

*I look at these; I think of all the common factors.*0144

*I know 1 is a common factor; 5 is a common factor.*0149

*15 is a common factor; those are all considered common factors.*0155

*But we are looking for the greatest common factor.*0159

*For this problem, the answer would be 15; the GCF is 15.*0163

*Another method to solve this would be to list out the two numbers.*0178

*Let's say 15 and 30 like this.*0184

*I am going to draw a little L shape around the two numbers.*0187

*From here, I just want to find any common factor, except for 1 of course.*0197

*Any common factor between the two numbers; let's say 5.*0204

*I am going to write that right outside the box.*0211

*If I pull 5 out of 15 or 15 divided by 5, I get 3.*0216

*I am going to write that right below the 15.*0224

*Right here, if I take a 5 out of 30 or 30 divided by 5, then I get 6.*0228

*I look at these two numbers, the two numbers that I just wrote, 3 and 6.*0237

*Do they have anything common?*0241

*I know that 3 can go into both of these numbers.*0244

*Since I know that they have a common factor, I am going to write another box under.*0248

*The common factor was 3.*0254

*I am going to write that common factor on the outside.*0259

*Again 3 divided by 3, if I pull a 3 out, it is going to be left with 1.*0263

*From 6, if I take a 3 out or 6 divided by 3, then I get 2.*0270

*I look at these two numbers, 1 and 2.*0279

*The only common factor between 1 and 2 is the number 1.*0281

*I am not going to consider 1 because all numbers have a common factor of 1.*0287

*So there, I am done.*0292

*I am going to take all the numbers that I have on the side.*0295

*5 and 3, I am going to circle them.*0300

*I am going to multiply them out; it is going to be 5 times 3.*0302

*My answer is 15; therefore my GCF is 15.*0307

*Let's do another example; I am going to be using method two.*0318

*If you want, you can pause the video; I want you to try both methods.*0323

*The first method was listing out all the factors for each number and then finding the greatest common one.*0327

*The second method was listing them out.*0335

*You are going to pull out one common factor at a time.*0337

*Then you are going to multiply all of those common factors.*0341

*Go ahead and pause; work on this problem right now.*0344

*I am going to use method two for these examples.*0350

*I am going to write out the two numbers, 6 and 18.*0356

*I am going to draw out this little L shape box around it.*0362

*I am going to think of a common factor; let's see, 6 and 18.*0367

*I know that they are both even numbers.*0374

*I am going to take out a 2.*0377

*Whenever they are both even numbers, they have a common factor of 2.*0381

*If I pull out a 2 from 6, that means I am going to do 6 divided by 2.*0387

*I am going to get 3; I write that right below the 6.*0393

*From 18, if I pull out a 2, 18 divided by 2, I get 9.*0400

*3 and 9, they do have a common factor.*0408

*I am going to draw another one of these; their common factor is 3.*0414

*If I do 3 divided by this number 3, then I get a 1.*0421

*I do 9 divided by 3; I get a 3.*0426

*Again these bottom numbers, 1 and 3, they only have a common factor of 1 which means that I am done.*0431

*I take these two numbers on the side.*0440

*You are going to take all the numbers; you are going to multiply them out.*0443

*It is going to be... the GCF of 6 and 18 is 2 times 3 which is going to be 6.*0446

*The next example with 36 and 27; these numbers are a little bit bigger.*0466

*You just have to take one common factor out.*0482

*We have 36; we have 27; let's see.*0485

*I know that 3 goes into 36 and 3 goes into 27.*0490

*I am going to take out a 3; 36 divided by 3 is 12.*0497

*27 divided by 3 is 9; again they have a common factor besides 1.*0509

*Draw another box; the common factor between 12 and 9 is 3.*0520

*When I divide 12 by 3, I get 4; 9 divided by 3 is 3.*0528

*With these two numbers, their only common factor is 1.*0537

*That means I no longer have to pull out common factors.*0541

*These two numbers on the side, I am going to multiply out.*0547

*The GCF is 9.*0550

*This next example with 4 and 42; they are both even numbers.*0560

*I can just take out a 2 because I know even numbers have a common factor of 2.*0575

*14 divided by 2 is 7; 42 divided by 2 is 21.*0582

*Do they have a common factor?*0591

*I think they do; we are going to draw this again.*0593

*We are going to pull out another common factor which is a 7.*0598

*7 divided by 7 is 1; 21 divided by 7 is 3.*0603

*Again they only have a common factor of 1.*0610

*That is when I take the numbers on the side.*0616

*I am going to multiply them out; the GCF is 14.*0619

*Last example, 54 and 36; again these numbers are a little big.*0631

*You can just think of a small common factor; these are both even numbers.*0645

*I know that a 2 goes into both of them.*0651

*I can just take that 2 out.*0654

*54 divided by 2 is 27; 36 divided by 2 is 18.*0658

*For this one, if you pull out another example, you will still get the same answer.*0672

*For example, a 6 goes into both of these numbers.*0678

*If you take out a 6, then your numbers are going to be different than mine.*0681

*But we will still get the same answer.*0685

*From these two numbers, 27 and 18, I know that a 3 goes into both.*0690

*27 divided by 3 is 9; 18 divided by 3 is 6.*0699

*9 and 6, they do have a common factor.*0710

*I have to do this one more time; their common factor is 3.*0714

*9 divided by 3 is 3; 6 divided by 3 is 2.*0719

*From these two numbers, 3 and 2, their common factor is 1.*0725

*That means I can take all the numbers on the side, not the bottom numbers, only the side.*0730

*I am going to multiply them out.*0738

*The GCF is going to be 3 times 3 times 2.*0740

*3 times 3 is 9; 9 times 2 is 18.*0749

*The GCF, the greatest common factor, between 54 and 36 is 18.*0755

*That was the lesson for greatest common factor.*0763

*Thank you for watching Educator.com.*0765

1 answer

Last reply by: Emil Poulsen

Sat Feb 11, 2017 10:48 AM

Post by Karina Herrera on December 28, 2016

For the example asking to find the GCF of 6 & 18, using the 2nd method, I used 3 instead of 2 as a common factor for the numbers but still got the same answer. Did I just get lucky, or have I missed something?

Thank you for the lessons by the way. They are very helpful. :)

1 answer

Last reply by: Don Ky

Sun Jun 7, 2015 8:34 PM

Post by Dante Danis on December 1, 2014

Super easy and simple. I loved the second method. Thank you again.

0 answers

Post by Milan Ray on April 16, 2014

your voice is hazy ????

0 answers

Post by Milan Ray on April 16, 2014

Another factor of 30 and15 is 3

1 answer

Last reply by: Mary Pyo

Thu Aug 2, 2012 10:37 PM

Post by Joseph Craft on July 26, 2012

Will you always have a common factor? What would be the common factor between 123 and 56

0 answers

Post by jimmy getachew on May 18, 2012

God bless you. I am a home schooling parent and you are making my life easy.

1 answer

Last reply by: Rocio Jackson

Thu Oct 4, 2012 11:55 PM

Post by David Nelson on March 21, 2012

Note: 3 is not the greatest common factor of 15 and 30

1 answer

Last reply by: faisal madar

Tue Nov 12, 2013 5:23 PM

Post by Angel Pina on February 11, 2012

What's the best way to find those numbers if I use method 1?

3 answers

Last reply by: carreola arreola

Tue Jul 24, 2012 2:55 PM

Post by judy lee on August 17, 2011

Isn't 3 a common factor of 15 and 30?