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### Greatest Common Factor

• 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

Find the GCF of 9 and 27
• 9 ×1 = 9, 9 ×3 = 27
9
Find the GCF of 8 and 24
• 8 ×1 = 8, 8 ×3 = 24
8
Find the GCF of 24 and 18
• 6 ×4 = 24, 6 ×3 = 18
6
Find the GCF of 72 and 64
• 8 ×9 = 72, 8 ×8 = 64
8
Find the GCF of 15 and 45
• 5 ×3 = 15, 5 ×9 = 45
• 3 ×1 = 3, 3 ×3 = 9
• 5 ×3
15
Find the GCF of 18 and 36
• 18 ×1 = 18,18 ×2 = 36
18
Find the GCF of 14 and 28
• 14 ×1 = 14, 14 ×2 = 28
14
Find the GCF of 12 and 30
• 6 ×2 = 12, 6 ×5 = 30
6
Find the GCF of 54 and 48
• 6 ×9 = 54, 6 ×8 = 48
6
Find the GCF of 49 and 56
• 7 ×7 = 49, 7 ×8 = 56
7

*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.

### 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

### 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