What is the GCF of 48?

Greatest common factor (GCF) of 48 and 56 is 8.

GCF(48,56) = 8

We will now calculate the prime factors of 48 and 56, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48 and 56.

We will first find the prime factorization of 48 and 56. After we will calculate the factors of 48 and 56 and find the biggest common factor number .

Step-1: Prime Factorization of 48

Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:

48 = 24 × 31

Step-2: Prime Factorization of 56

Prime factors of 56 are 2, 7. Prime factorization of 56 in exponential form is:

56 = 23 × 71

Step-3: Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24

Step-4: Factors of 56

List of positive integer factors of 56 that divides 48 without a remainder.

1, 2, 4, 7, 8, 14, 28

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48 and 56. The biggest common factor number is the GCF number.
So the greatest common factor 48 and 56 is 8.

Also check out the Least Common Multiple of 48 and 56

Are you on the hunt for the GCF of 48, 48, 64, and 80? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now!

First off, if you're in a rush, here's the answer to the question "what is the GCF of 48, 48, 64, and 80?":

GCF of 48, 48, 64, and 80 = 16

What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

Greatest Common Denominator (GCD)
Highest Common Factor (HCF)
Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them.

For 48, 48, 64, and 80 those factors look like this:

Factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Factors for 64: 1, 2, 4, 8, 16, 32, and 64
Factors for 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80

As you can see when you list out the factors of each number, 16 is the greatest number that 48, 48, 64, and 80 divides into.

Prime Factors

As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.

List out all of the prime factors for each number:

Prime Factors for 48: 2, 2, 2, 2, and 3
Prime Factors for 64: 2, 2, 2, 2, 2, and 2
Prime Factors for 80: 2, 2, 2, 2, and 5

Now that we have the list of prime factors, we need to find any which are common for each number.

Looking at the occurences of common prime factors in 48, 48, 64, and 80 we can see that the commonly occuring prime factors are 2, 2, 2, and 2.

To calculate the prime factor, we multiply these numbers together:

GCF = 2 x 2 x 2 x 2 = 16

Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 48, 48, 64, and 80 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!)

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Are you on the hunt for the GCF of 48 and 100? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now!

First off, if you're in a rush, here's the answer to the question "what is the GCF of 48 and 100?":

GCF of 48 and 100 = 4

What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

Greatest Common Denominator (GCD)
Highest Common Factor (HCF)
Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them.

For 48 and 100 those factors look like this:

Factors for 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Factors for 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100

As you can see when you list out the factors of each number, 4 is the greatest number that 48 and 100 divides into.

Prime Factors

List out all of the prime factors for each number:

Prime Factors for 48: 2, 2, 2, 2, and 3
Prime Factors for 100: 2, 2, 5, and 5

Now that we have the list of prime factors, we need to find any which are common for each number.

Looking at the occurences of common prime factors in 48 and 100 we can see that the commonly occuring prime factors are 2 and 2.

To calculate the prime factor, we multiply these numbers together:

GCF = 2 x 2 = 4

Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 48 and 100 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

GCF of 48 and 64 is the largest possible number that divides 48 and 64 exactly without any remainder. The factors of 48 and 64 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 48 and 64 - Euclidean algorithm, long division, and prime factorization.

What is GCF of 48 and 64?

Answer: GCF of 48 and 64 is 16.

Explanation:

The GCF of two non-zero integers, x(48) and y(64), is the greatest positive integer m(16) that divides both x(48) and y(64) without any remainder.

Methods to Find GCF of 48 and 64

The methods to find the GCF of 48 and 64 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 48 and 64 by Listing Common Factors

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 5 common factors of 48 and 64, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 48 and 64 is 16.

GCF of 48 and 64 by Prime Factorization

Prime factorization of 48 and 64 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 48 and 64 have common prime factors. Hence, the GCF of 48 and 64 is 2 × 2 × 2 × 2 = 16.

GCF of 48 and 64 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 64 and Y = 48

GCF(64, 48) = GCF(48, 64 mod 48) = GCF(48, 16)
GCF(48, 16) = GCF(16, 48 mod 16) = GCF(16, 0)
GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 48 and 64 is 16.

☛ Also Check:

GCF of 48 and 64 Examples

Example 1: For two numbers, GCF = 16 and LCM = 192. If one number is 48, find the other number.

Solution:

Given: GCF (z, 48) = 16 and LCM (z, 48) = 192 ∵ GCF × LCM = 48 × (z) ⇒ z = (GCF × LCM)/48 ⇒ z = (16 × 192)/48 ⇒ z = 64
Therefore, the other number is 64.

Example 2: Find the GCF of 48 and 64, if their LCM is 192.

Solution:

∵ LCM × GCF = 48 × 64 ⇒ GCF(48, 64) = (48 × 64)/192 = 16

Therefore, the greatest common factor of 48 and 64 is 16.

Example 3: The product of two numbers is 3072. If their GCF is 16, what is their LCM?

Solution:

Given: GCF = 16 and product of numbers = 3072 ∵ LCM × GCF = product of numbers ⇒ LCM = Product/GCF = 3072/16

Therefore, the LCM is 192.

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The GCF of 48 and 64 is 16. To calculate the GCF of 48 and 64, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 48 and 64, i.e., 16.

How to Find the GCF of 48 and 64 by Long Division Method?

To find the GCF of 48, 64 using long division method, 64 is divided by 48. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 48, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 48 and 64, i.e. GCF × LCM = 48 × 64.

What are the Methods to Find GCF of 48 and 64?

There are three commonly used methods to find the GCF of 48 and 64.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 64 and 48 is 16, Find its LCM.

GCF(64, 48) × LCM(64, 48) = 64 × 48 Since the GCF of 64 and 48 = 16 ⇒ 16 × LCM(64, 48) = 3072 Therefore, LCM = 192

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How to Find the GCF of 48 and 64 by Prime Factorization?

To find the GCF of 48 and 64, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2. ⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 48 and 64. Hence, GCF(48, 64) = 2 × 2 × 2 × 2 = 16

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