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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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
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?