How to Find the GCF and LCM using Prime Factorization | Math with Mr. J (2023)

Introduction

Welcome to How to Find the GCF (aka HCF) and LCM using Prime Factorization with Mr. J! Need help with how to find the greatest common factor (aka highest common factor) and least common multiple using prime factorization? You're in the right place!

Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with finding the GCF and LCM. Mr. J will go through examples of finding the greatest common factor using prime factorization and examples of finding the least common multiple using prime factorization.

MORE VIDEOS ON RELATED TOPICS:

✅ Greatest Common Factor
- Factors, Common Factors, and Greatest Common Factor = youtu.be/IRHwkNBpG_Q
- How to find the Greatest Common Factor = youtu.be/vBcmH5TmTxM
- Greatest Common Factor of 3 Numbers = youtu.be/jskvFR61lBE
- Greatest Common Factor of 3 Numbers (Part 2) = youtu.be/XcsQs95yNGc
- Greatest Common Factor Using Prime Factorization = youtu.be/LDx95tyBtQ8
- Greatest Common Factor of 3 Numbers Using Prime Factorization = youtu.be/0YYRxTGmey8

✅ Least Common Multiple
- Multiples, Common Multiples, and Least Common Multiple = youtu.be/qs0I6aQu4cY
- How to Find the Least Common Multiple = youtu.be/gBgXbFiwVT0
- Least Common Multiple of 3 Numbers = youtu.be/GPqUeSoTHeU
- Least Common Multiple of 3 Numbers (Part 2) = youtu.be/uZFCTV6Xq2s
- Least Common Multiple Using Prime Factorization = youtu.be/L6n0ZkwueOM
- Least Common Multiple of 3 Numbers Using Prime Factorization = youtu.be/Zh6FZgvOEv0

✅ Factors and Multiples Combined
- Factors & Multiples | Common Factors & Multiples | Greatest Common Factor & Least Common Multiple = youtu.be/N_S_wrN8ue8
- Greatest Common Factor and Least Common Multiple = youtu.be/zvaxUJOv6jM
- How to Find the Greatest Common Factor and Least Common Multiple of 3 Numbers = youtu.be/L0hqNNq_Aq4
- How to Find the Greatest Common Factor and Least Common Multiple of 3 Numbers (Part 2) = youtu.be/9epOXxJVKV4
- Greatest Common Factor and Least Common Multiple Using Prime Factorization = youtu.be/Veo6jftWyNw
- Greatest Common Factor and Least Common Multiple of 3 Numbers Using Prime Factorization = youtu.be/dzU8JJhqaso

About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. #MathWithMrJ

Click Here to Subscribe to the Greatest Math Channel On Earth: goo.gl/XHTrfY

Follow Mr. J on Twitter: @MrJMath5

Email: math5.mrj@gmail.com

Music: www.bensound.com/royalty-free-music

Hopefully this video is what you're looking for when it comes to finding the greatest common factor using prime factorization and finding the least common multiple using prime factorization.

Have a great rest of your day and thanks again for watching! ✌️✌️✌️

✅ Thanks to Aloud, this video has been dubbed into Spanish and Portuguese. #DubbedWithAloud

English
This video has been dubbed into Spanish (United States) and Portuguese (Brazil) using an artificial voice via aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu.

Spanish
Este video ha sido doblado al español con voz artificial con aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración.

Portuguese
Este vídeo foi dublado para o português usando uma voz artificial via aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações.

Video

Welcome to math with Mr J in this video I'm going to cover how to find the greatest common factor and least common multiple using prime factorization now, I like using prime factorization and find it helpful when working with numbers that are a little larger in value and not as simple to work with, for example, the strategy of listing out all of the factors or listing some multiples of the numbers you're working with can be kind of difficult and time consuming when working with larger numbers in value.

So prime factorization is a different approach, a different strategy to be familiar with when it comes to finding the greatest common factor or least common multiple let's, start with the greatest common factor and jump into our examples, starting with number one, where we have 63 and 84.

let's start with the prime factorization of 6 63.

And we will start with the factors of 7 and nine seven times nine equals sixty-three so seven and nine are factors of 63.

Now 7 is prime.

So we are done there nine.

We can break down three times three equals nine.

So three is a factor of nine.

Three is prime.

So we are done there and there and that's the prime factorization of 63.

We can't break that down any further.

Now we have the prime factorization of 84.

let's start with the factors of 2 and 42 2 times 42 equals Eighty-Four so 2 and 42 are factors of 84.

Now 2 is prime.

So we are done there 42.

We can break down 2 times, 21 equals 42.

so 2 and 21 are factors of 42.

2 is prime.

So we are done there 21.

We can break down three times seven equals twenty one.

So three and seven are factors of 21.

three is prime and 7 is prime as well.

So we are done that's the prime factorization of 84.

We can't break that down any further now that we have the prime factorization of both of those numbers.

We need to find common prime factors.

So prime factors that they share now I'm going to list the prime factors of each to make it easier to find the ones they have in common.

So as far as 63, we have three three and seven three times three times, seven equals 63.

484.

We have two two three and seven two times two times three times seven equals 84.

Now we need to find any common prime factors.

Three is a common prime factor and 7 is a common prime factor.

So they have a 3 and a 7 in common.

Once we find those common prime factors.

We multiply them so three times 7, and that equals 21 and that's, our greatest common factor.

So the GCF, the greatest common factor of 63, and 84 is 21.

let's move on to number two where we have 48 and 72.

let's start with the prime factorization of 48.

And we will start with the factors of 2 and 24.

2 times 24 equals 48.

So they are factors.

Now 2 is prime.

So we are done there.

We can break down 24.

2 times 12 equals 24 so 2 and 12 are factors 2 is prime.

So we are done there.

We can break 12 down further 2 times 6 equals 12 so 2 and 6 are factors 2 is prime.

So we are done there, but we can break 6 down further 2 times 3 equals 6 so 2 and 3 are factors 2 is prime.

So we are done there and 3 is prime.

So we are done there as well.

And we are done with the prime factorization of 48.

We can't break that down any further.

Now we need the prime factorization of 72.

let's start with the factors of 2 and 36 2 times 36 equals 72.

So they are factors 2 is prime.

So we are done here.

36.

We can break down 2 times 18 equals 36.

So 2 and 18 are factors 2 is prime.

So we are done there.

18.

We can break down 2 times 9 equals 18 so 2 and 9 are factors 2 is prime.

So we are done there, but we can break nine down further three times three equals nine.

So 3 is a factor of nine.

Three is prime.

So we are done there and there, and we are done with the prime factorization of 72.

We can't break that down any further now that we have the prime factorization of both 48 and 72, we need to find common prime factors.

So I'm going to write the prime factors of 48 and 72 that way, it's a little easier to find common prime factors for 48.

We have two two and three.

So two times two times two times two times three equals 48 472.

We have two two two three and three two times two times two times three times three equals 72.

Now we need to find common prime factors.

They have a 2 in common another two in common another two in common, and then a three in common.

So now that we found the common prime factors we need to multiply them to get the greatest common factor.

So we have two times two times two.

They have three twos in common times.

Three, two times two is four times two is eight times three is 24.

So the GCF, the greatest common factor of 48 and 72 is 24.

so there's how we use prime factorization in order to find the greatest common factor, let's move on to least common multiple.

Here are our examples for finding the least common multiple using prime factorization, let's jump into our examples, starting with number one, where we have 15 and 27.

let's start with the prime factorization of 15, and we will start with the factors of 3 and five.

Now three is prime.

So we are done there and 5 is prime.

So we are done there as well and that's the prime factorization of 15.

We can't break that down any further.

Now we have the prime factorization of 27.

let's start with the factors of 3 and 9.

3 times 9 equals 27 so 3 and 9 are factors of 27.

3 is prime.

So we are done there, but we can break 9 down 3 times 3 equals nine.

So three is a factor of nine.

Three is prime.

So we are done there and there and that's the prime factorization of 27.

We can't break that down any further now, we're ready to move to the next step.

So we need to list the prime factors of 15 and 27 and match them.

Vertically, let's, see what this looks like starting with 15.

So our prime factors from the prime factorization are three and five or three times five now, four twenty-seven.

So we have three times three times three and you'll.

Notice that big gap underneath the 5 there we are matching numbers.

Vertically, 27 does not have a prime factor of five.

So I left that blank underneath the 5.

now that we have our prime factors listed and matched vertically.

We move on to the next step where we bring down and I like to draw a line underneath here in order to separate these steps.

So this is a column.

And although we have two threes here, this is a column of Threes.

So we just bring one down.

We have a three to represent that column of two threes times.

We have a column of five here times.

We have a three here times another three here.

So we end up with three times five times three times three and by multiplying these we get our least common multiple.

So three times five is fifteen times three is forty-five times.

Three is one hundred thirty-five and that's, our least common multiple.

So the LCM, the least common multiple of 15 and 27 is one hundred thirty-five, let's move on to number two where we have 28 and 52.

let's start with the prime factorization of 28.

Now 2 times 14 equals 28.

So let's start with those factors 2 is prime.

So we are done there 14.

We can break down two times seven equals 14.

so 2 and 7 are factors of 14.

2 is prime.

So we are done there and 7 is prime as well.

So we are done there and that's the prime factorization of 28.

We can't break that down any further.

Now we need the prime factorization of 52.

let's start with the factors of 2 and 26 2 times 26 equals 52.

so 2 and 26 are factors of 52.

2 is prime.

So we are done there 26.

We can break that down 2 times 13 equals 26.

So 2 and 13 are factors of 26.

2 is prime.

So we are done there and 13 is prime as well.

So we are done there and that's the prime factorization of 52.

We can't break that down any further.

Now we need to list the prime factors and match them vertically, 428.

We have 2 times 2 times 7.

452.

We have two times two times 13.

Now we need to bring down.

So we have a column of twos here.

So let's bring down a 2 to represent that column times another column of twos.

So let's bring another two down times 7 times 13.

So we have 2 times 2 times 7 times 13 to get our least common multiple.

We have two times two, which is 4 times 7 is 28 times, 13., well, I'm, not sure what 28 times 13 is so let's come to the side here and multiply 28 times 13.

We will start with 3 times 8, which is 24 3 times 2 is 6 Plus 2.

is eight.

We are done here and done here.

We need a zero.

Now we have one times eight, which is eight.

And then one times two is two let's.

Add four, plus zero is four eight, plus eight is sixteen.

And then one plus two is three.

So we get 364.

So the least common multiple of 28 and 52.

Let me squeeze this in here is 300 60 4.

So there you have it there's how to find the greatest common factor, the GCF and least common multiple the LCM using prime factorization, I hope that helped thanks so much for watching until next time.

Peace.