# 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

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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! ✌️✌️✌️

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## 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.

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.

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.

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.

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.

Now 2 times 14 equals 28.

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.

## FAQs

### How to find its greatest common factor GCF using prime factorization? ›

Steps on How to Determine the GCF using Prime Factorization
• Write the Prime Factorization of each number. ...
• Identify the numbers that have the same base. ...
• Compare the exponents of the numbers with a common base. ...
• Multiply the numbers that you selected in step #3 to determine the greatest common factor.

What is the GCD and LCM of a number by prime factorization? ›

The lowest common multiple is the smallest number that has all the prime factors from both numbers. Thus, the gcd of two numbers is the largest part of their prime factorization that they have in common. The lcm of two numbers is the number which has all the prime factors from both numbers and no other factors.

How to find HCF and LCM of two numbers by prime factorization method? ›

To find the HCF, find any prime factors that are in common between the products. Each product contains two 2s and one 3, so use these for the HCF. Cross any numbers used so far off from the products. To find the LCM, multiply the HCF by all the numbers in the products that have not yet been used.

How do you use prime factorization to find the GCF of each pair of Monomials? ›

To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam! The GCF!

What are the two methods in finding the GCF and LCM? ›

There are a variety of techniques for finding the LCM and GCF. The two most common strategies involve making a list, or using the prime factorization. For example, the LCM of 5 and 6 can be found by simply listing the multiples of 5 and 6, and then identifying the lowest multiple shared by both numbers.

What is GCF and LCM example? ›

In other words, it's the number that contains all the factors *common* to both numbers. In this case, the GCF is the product of all the factors that 2940 and 3150 share. On the other hand, the Least Common Multiple, the LCM, is the smallest (that is, the "least") number that both 2940 and 3150 will divide into.

What are the 3 ways to find the greatest common factor? ›

To calculate GCF, there are three common ways- division, multiplication, and prime factorization.

How do you calculate LCM step by step? ›

Step 1: Find the prime factors of the given numbers by repeated division method. Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power. Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

How to use the prime factorization of each number to find the greatest common factor of 24 and 54? ›

Prime factorization of 24 and 54 is (2 × 2 × 2 × 3) and (2 × 3 × 3 × 3) respectively. As visible, 24 and 54 have common prime factors. Hence, the GCF of 24 and 54 is 2 × 3 = 6.

How can you use the prime factorization method to find the LCM of the following groups of numbers 4 8 and 16? ›

Prime factorization of 4, 8, and 16 is (2 × 2) = 22, (2 × 2 × 2) = 23, and (2 × 2 × 2 × 2) = 24 respectively. LCM of 4, 8, and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 = 16. Hence, the LCM of 4, 8, and 16 by prime factorization is 16.

### What is the GCF of 12 and 20 using prime factorization? ›

GCF of 12 and 20 by Prime Factorization

Prime factorization of 12 and 20 is (2 × 2 × 3) and (2 × 2 × 5) respectively. As visible, 12 and 20 have common prime factors. Hence, the GCF of 12 and 20 is 2 × 2 = 4.

What is the GCF of 36 and 60 using prime factorization? ›

GCF of 36 and 60 by Prime Factorization

As visible, 36 and 60 have common prime factors. Hence, the GCF of 36 and 60 is 2 × 2 × 3 = 12.

What is the GCF of 30 and 80 using prime factorization? ›

The GCF of 30 and 80 is 10. To calculate the greatest common factor of 30 and 80, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 30 and 80, i.e., 10.

How do you find the greatest common factor GCF of the given numbers? ›

To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

What is the GCF of 18 and 20 using prime factorization? ›

How to Find the GCF of 18 and 20 by Prime Factorization? To find the GCF of 18 and 20, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 20 = 2 × 2 × 5. ⇒ Since 2 is the only common prime factor of 18 and 20. Hence, GCF (18, 20) = 2.

What is the GCF and LCM of 18 and 20 using prime factorization? ›

LCM of 18 and 20 by Prime Factorization

LCM of 18 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 × 51 = 180. Hence, the LCM of 18 and 20 by prime factorization is 180.

What is the GCF of 15 and 20 using prime factorization? ›

GCF of 15 and 20 by Prime Factorization

Prime factorization of 15 and 20 is (3 × 5) and (2 × 2 × 5) respectively. As visible, 15 and 20 have only one common prime factor i.e. 5. Hence, the GCF of 15 and 20 is 5.

What is the GCF of 24 and 64 using prime factorization? ›

The GCF of 24 and 64 is 8. To calculate the GCF (Greatest Common Factor) of 24 and 64, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 24 and 64, i.e., 8.

What is the GCF of 18 and 60 using prime factorization? ›

HCF of 18 and 60 by Prime Factorisation Method

HCF (18, 60) = 2 × 3 = 6.

What is the GCF of 63 and 45 using prime factorization? ›

What is the GCF of 45 and 63? The GCF of 45 and 63 is 9. To calculate the greatest common factor of 45 and 63, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 45 and 63, i.e., 9.

### What is the GCF of 30 and 42 using prime factorization? ›

GCF of 30 and 42 by Prime Factorization

Prime factorization of 30 and 42 is (2 × 3 × 5) and (2 × 3 × 7) respectively. As visible, 30 and 42 have common prime factors. Hence, the GCF of 30 and 42 is 2 × 3 = 6.

What is the GCF of 40 and 30 using prime factorization? ›

GCF of 30 and 40 by Prime Factorization

Prime factorization of 30 and 40 is (2 × 3 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 30 and 40 have common prime factors. Hence, the GCF of 30 and 40 is 2 × 5 = 10.

What is the GCF of 24 and 30 using prime factorization? ›

GCF of 24 and 30 by Prime Factorization

Prime factorization of 24 and 30 is (2 × 2 × 2 × 3) and (2 × 3 × 5) respectively. As visible, 24 and 30 have common prime factors. Hence, the GCF of 24 and 30 is 2 × 3 = 6.

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