Greatest Common Factor | How to Find the Greatest Common Factor (GCF)

Summary

In this educational video, Mr. J teaches viewers how to determine the greatest common factor (GCF) of two numbers. The process involves listing all factors of each number and identifying the largest factor they share. Mr. J walks through several examples, starting with 10 and 15, then 12 and 6, and finally 20 and 10, and 9 and 21, demonstrating the method for both even and odd numbers. The video is designed to help students understand the concept of factors and how to apply them to find the GCF effectively.

Takeaways

• 📚 The video is a math lesson focused on finding the greatest common factor (GCF) of two numbers.
• 🔢 A factor is a number that can multiply together to give another number.
• 👉 To find the GCF, list all factors of each number and identify the largest common one.
• 🌰 The example given starts with the numbers 10 and 15, and the factors of 10 are 1, 2, 5, and 10.
• 📝 For the number 15, the factors are 1, 3, 5, and 15, with 5 being the GCF with 10.
• 🧩 The video demonstrates the process with additional examples, such as 12 and 6, where the GCF is 6.
• 🤔 It encourages viewers to try some problems on their own before revealing the solution.
• 📉 For the numbers 20 and 10, the factors are listed, and the GCF is found to be 10.
• 🤹‍♂️ The lesson includes a mix of even and odd numbers, like 9 and 21, with 3 as their GCF.
• 📝 The importance of using the list of factors already known, like recognizing 10's factors from the previous example, is emphasized.
• 🎓 The video concludes by summarizing the concept of GCF and thanking viewers for watching.

Q & A

What is the main topic of the video?

The main topic of the video is how to find the greatest common factor (GCF) between two numbers.

What is a factor according to the video?

A factor is a number that can multiply together to give you another number.

How does the video suggest listing the factors of a number?

The video suggests starting with 1 and the number itself, then listing other factors in between, with pairs that multiply to give the original number.

What is the greatest common factor of 10 and 15 according to the video?

The greatest common factor of 10 and 15 is 5.

What factors does the video list for the number 12?

The factors listed for 12 are 1, 2, 3, 4, 6, and 12.

What is the greatest common factor of 12 and 6?

The greatest common factor of 12 and 6 is 6.

How does the video approach finding the GCF for 20 and 10?

The video lists the factors of 20 (1, 2, 4, 5, 10, 20) and 10 (1, 2, 5, 10) and identifies the greatest common factor, which is 10.

What is the greatest common factor of 9 and 21 as per the video?

The greatest common factor of 9 and 21 is 3.

What is the significance of listing factors in pairs according to the video?

Listing factors in pairs helps to visualize and understand how different numbers can multiply to give the original number.

Why does the video mention that spacing is not as important when listing factors?

The video mentions that as long as all the factors are listed, the exact spacing between them is not crucial for finding the GCF.

What is the video's advice for finding the GCF when one of the numbers is prime?

The video suggests that if one of the numbers is prime, you will only have 1 and that prime number itself as factors, which simplifies the process of finding the GCF.

Outlines

00:00

📚 Introduction to Finding the Greatest Common Factor

In the first paragraph, Mr. J introduces the concept of finding the greatest common factor (GCF) of two numbers. He explains the meaning of a factor and demonstrates the process of listing all factors for the numbers 10 and 15. Mr. J emphasizes the importance of understanding factors as numbers that multiply to give the original number. For 10, the factors are 1, 2, 5, and 10, with 2 and 5 being a pair that multiplies to 10. For 15, the factors are 1, 3, 5, and 15, with 3 and 5 being a pair. The GCF for the pair 10 and 15 is identified as 5, as it is the highest number common to both sets of factors.

05:01

🔍 Continuing the Exploration of the Greatest Common Factor

The second paragraph continues the discussion on finding the GCF, focusing on the sets of numbers 12 and 6, and then 20 and 10. Mr. J illustrates the process of listing factors for each number, pointing out that 12 has factors of 1, 2, 3, 4, 6, and 12, while 6 has factors of 1, 2, 3, and 6. The GCF for 12 and 6 is determined to be 6, as it is the highest common factor. Moving on to 20 and 10, the factors of 20 are listed as 1, 2, 4, 5, 10, and 20, and for 10, they are 1, 2, 5, and 10. The GCF for these numbers is 10, as it is the largest number present in both sets of factors. The paragraph concludes with an example involving the odd numbers 9 and 21, where the GCF is found to be 3, since it is the highest common factor between the two sets of factors.

Keywords

💡Greatest Common Factor (GCF)

The Greatest Common Factor, also known as the Greatest Common Divisor, is the largest positive integer that divides two or more numbers without leaving a remainder. In the video, Mr. J explains how to find the GCF of different pairs of numbers, which is central to the theme of the video. For example, the GCF of 10 and 15 is 5, as it is the highest number that divides both 10 and 15 evenly.

💡Factors

Factors are the numbers that multiply together to produce another number. In the context of the video, Mr. J demonstrates listing the factors of numbers such as 10 and 15 to find their GCF. The factors of 10 are 1, 2, 5, and 10, which are all the numbers that can be multiplied together in pairs to give the product of 10.

💡Composite Numbers

Composite numbers are positive integers that have at least one divisor other than 1 and the number itself. In the script, Mr. J mentions that 15 is a composite number because it has factors other than 1 and 15, specifically 3 and 5, which when multiplied together give 15.

💡Prime Numbers

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The script implies the concept of prime numbers when discussing factors, noting that if a number is prime, it will only have two factors: 1 and the number itself.

💡Multiplication Fact

A multiplication fact refers to a basic arithmetic relationship where two numbers are multiplied together to produce a product. In the video, Mr. J uses multiplication facts to identify factors, such as '1 times 10 equals 10' or '2 times 5 equals 10', to demonstrate how factors are found.

💡Even Numbers

Even numbers are integers that are exactly divisible by 2. In the script, Mr. J identifies even numbers as a starting point for listing factors because they can be divided by 2. For instance, when listing factors for 12 and 6, he starts with 2 because both numbers are even.

💡Odd Numbers

Odd numbers are integers that are not divisible by 2, leaving a remainder of 1 when divided by 2. The video script discusses odd numbers in the context of finding the GCF of 9 and 21, which are both odd and do not start with the factor 2.

💡Pairs

In the context of factors, pairs refer to two numbers that multiply together to form the original number. Mr. J uses the term 'pairs' to describe factor pairs, such as 2 and 5 for the number 10, which when multiplied give the product of 10.

💡Divisibility

Divisibility is the property of a number being able to be divided by another number without leaving a remainder. The concept of divisibility is central to the video's theme, as it is used to determine factors and subsequently the GCF. For example, 10 is divisible by 2 and 5, which are factors of 10.

💡Common Factors

Common factors are the factors that two or more numbers share. In the video, Mr. J identifies common factors between pairs of numbers to find the GCF. For instance, both 12 and 6 have 6 as a common factor, making 6 the GCF of these two numbers.

💡Arithmetic

Arithmetic refers to the branch of mathematics that deals with the study of numbers and basic operations like addition, subtraction, multiplication, and division. The video's content is fundamentally arithmetic, as it focuses on multiplication to find factors and GCFs of numbers.

Highlights

Introduction to the concept of finding the greatest common factor (GCF) between two numbers.

Explanation of what a factor is and how to list factors of a number.

Demonstration of listing factors for the number 10, including 1, 2, 5, and 10.

Identification of 2 and 5 as factor pairs for the number 10.

Listing factors for the number 15, including 1, 3, 5, and 15.

Discussion on the difference between prime and composite numbers in relation to factors.

Finding the GCF of 10 and 15, which is 5.

Listing factors for 12, including 1, 2, 3, 4, 6, and 12.

Listing factors for 6, including 1, 2, and 3.

Determining the GCF of 12 and 6, which is 6.

Listing factors for 20, including 1, 2, 4, 5, 10, and 20.

Listing factors for 10, using the previously listed factors for quick reference.

Finding the GCF of 20 and 10, which is 10.

Listing factors for 9, which includes only 1, 3, and 9 due to it being a square number.

Listing factors for 21, including 1, 3, 7, and 21.

Determining the GCF of 9 and 21, which is 3.

Conclusion of the video with a summary of the GCF process and a thank you to the viewers.

Transcripts

welcome to math with mr. J in this video

we're going to discuss how to find the

greatest common factor between two

numbers and as you can see there are

four problems here and sets of numbers

that we're going to find the greatest

common factor so for example number one

we have ten and fifteen so let's jump

right into that one and see how we find

the greatest common factor well before

we find the greatest common factor we

need to know what factor means and a

factor our factors are all the numbers

that can multiply together to give you

that number so let's make sense of this

so we have ten here we're going to list

all the factors of ten and like I said

it's all the numbers that can multiply

together to give you ten so for every

number when you're listing the factors

you can start with two things one and

that number itself and I'm going to put

some space in between for the other

factors these are our factor pair here

because I can do 1 times 10 equals 10 or

10 times 1 that's a multiplication fact

that gives me 10 so those are factors

can you think of any other pairs that

will equal 10 hopefully you're thinking

2 & 5 right 2 times 5 is 10 or 5 times 2

is 10 so I fill in my space here with

the 2 and the 5 and 10 has 4 factors 1 2

5 & 10 2 & 5 are a pair as well if you

want to connect them if that helps you

out that works so let's do 15 so we need

to think of the factors of 15 so we

always start with 1 and the number

itself and leave some space in between

for your other factors now once you get

better at this you will get very good at

the spacing when you're

starting out you may have trouble

spacing out in between there where you

can put your factors that's fine as long

as you have all your factors listed

don't worry so much about the spacing so

one in 15 now sometimes if the numbers

prime you'll only have a 1 and that

number itself that's what exactly what

prime means but composite numbers means

means you have more than just one and

the number itself and 15s composites so

can we think of another any other

factors for 15 hopefully we are thinking

3 & 5 right 3 times 5 is 15 so 3 & 5 are

pair 1 and 15 are pair and there aren't

anymore so we're done so now we need to

find the greatest common factor so the

greatest one that they have in common so

I see that they have one in common and

they also have 5 in common so what's the

greatest well 5 so we could put GCF

greatest common factor equals 5 all

right let's try number 2 here so we have

12 + 6 let's start with our factors of

12 so we start with 1 & 12

well 12s even so I know 2 is going to be

a factor and you can think well what's

what's twos partner well 6 2 times 6

gives me 12 so put my 6 here and there's

one more pair or two more factors for 12

and it's 3 & 4 and that's it for 12 now

let's write our factors for 6 so we

always start with 1 and the number

itself 6 is even so I know 2 is

automatically going to be a factor and

twos partner or other factor for 6 is 3

here so there's your

list of factors for six so I see they

have one in common and sometimes that

will be your answer for greatest common

factor not for number two here well

speaking of two they have two in common

three in common and they also have six

in common so they have a lot of common

factors but we want the greatest so the

GCF for 12 and six is going to be six

all right number three and four here if

you feel comfortable enough to try a

couple on your own feel free to press

pause finish three and four and then

when you're ready press play and check

your work with mine if you want to do

three and four with me that's fine as

well so let's do 20 and 10 so we'll

start with 1 and 20 and I know that 20s

even so 2 is going to be a factor and

its partners 10 any others well 4 and 5

and that's actually yet for 20 so let's

do 10 1 and 10 and when you get into

greatest common factors one thing you

should look for is if you already have a

list of something use it and we know

that 10 is 1 2 5 and 10 notice my

spacing wasn't great on that one I have

a lot of extra space here that's fine I

have all my factors listed and that's

that's the most important part so I see

that one - they have 5 in common and

then they have 10 in common so the GCF

is 10 for 20 and 10

alright lastly number four we have two

odd numbers here 9 and 21

so let's write our factors so 4 9 we'll

start with one and nine and then is

there anything else that we can multiply

to get 9 well 3 times 3 so 3 is a factor

you only need to write 3 once though 21

I'll start with 1 and 21 now are there

any factors of 21 other than 1 in 21 yes

3 times 7 so there are our factors for 9

and 21 they have one in common and they

also have 3 in common so the GCF or

greatest common factor is going to be 3

so there you have it there's greatest

common factor hopefully that helped

thanks so much for watching

until next time peace

you