Greatest Common Factor | How to Find the Greatest Common Factor (GCF)
Summary
TLDRIn 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
📚 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.
🔍 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.
Mindmap
Keywords
💡Greatest Common Factor (GCF)
💡Factors
💡Composite Numbers
💡Prime Numbers
💡Multiplication Fact
💡Even Numbers
💡Odd Numbers
💡Pairs
💡Divisibility
💡Common Factors
💡Arithmetic
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
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