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# what is the greatest common factor of 4 and 10

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### James

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## What is the greatest common factor of 4 and 10?

The greatest common factor is 2. First, you can list all the factors of 4. 1, 2, 4 Next, list all the factors of 10: 1, 2, 5, 10 Now, look back at the two lists and see if any of the numbers are the same in both lists. If there is more than one, the greatest number will be the greatest common factor. In this case, the only common number is 2, and so it is automatically the greatest common factor.

## What is the greatest common factor of 4 and 10?

Prealgebra Factors and Multiples Greatest Common Factor

Lydia · EZ as pi Mar 29, 2016

The greatest common factor is 2.

### Explanation:

First, you can list all the factors of 4.

1 , 2 , 4

Next, list all the factors of 10:

1 , 2 , 5 , 10

Now, look back at the two lists and see if any of the numbers are the same in both lists. If there is more than one, the greatest number will be the greatest common factor. In this case, the only common number is 2, and so it is automatically the greatest common factor.

EZ as pi Aug 24, 2016 The GCF = 2.

Both 4 and 10 are even, so they must have a common factor of 2.

In this case this is the only common factor (apart from 1).

### Explanation:

A good approach for any question involving factors, GCF, LCM and roots is to write each number as the product of its prime factors .

If you have a number written as the product of its prime factors, then you know everything about that number!

× . × x 4 = 2 × 2 × × x 10 = 2 × x × 5 × x G C F = 2

We can see that 2 is common to both.

This is also a good way of finding the LCM, especially of big numbers.

L C M = 2 × 2 × 5 = 20 Answer link

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## GCF of 4 and 10

GCF of 4 and 10 is the largest possible number which divides 4 and 10 without leaving any remainder. The methods to compute the GCF of 4, 10 are explained here.

## GCF of 4 and 10

GCF of 4 and 10 is the largest possible number that divides 4 and 10 exactly without any remainder. The factors of 4 and 10 are 1, 2, 4 and 1, 2, 5, 10 respectively. There are 3 commonly used methods to find the GCF of 4 and 10 - prime factorization, long division, and Euclidean algorithm.

## What is GCF of 4 and 10?

Answer: GCF of 4 and 10 is 2.Explanation:

The GCF of two non-zero integers, x(4) and y(10), is the greatest positive integer m(2) that divides both x(4) and y(10) without any remainder.

## Methods to Find GCF of 4 and 10

Let's look at the different methods for finding the GCF of 4 and 10.

Listing Common Factors

Long Division Method

Prime Factorization Method

### GCF of 4 and 10 by Listing Common Factors

Factors of 4: 1, 2, 4Factors of 10: 1, 2, 5, 10

There are 2 common factors of 4 and 10, that are 1 and 2. Therefore, the greatest common factor of 4 and 10 is 2.

### GCF of 4 and 10 by Long Division

GCF of 4 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10 (larger number) by 4 (smaller number).Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (2).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 4 and 10.

### GCF of 4 and 10 by Prime Factorization

Prime factorization of 4 and 10 is (2 × 2) and (2 × 5) respectively. As visible, 4 and 10 have only one common prime factor i.e. 2. Hence, the GCF of 4 and 10 is 2.

☛ Also Check:

GCF of 40 and 56 = 8

GCF of 15 and 50 = 5

GCF of 33 and 66 = 33

GCF of 30 and 36 = 6

GCF of 10, 30 and 45 = 5

GCF of 9 and 24 = 3

GCF of 36 and 100 = 4

## GCF of 4 and 10 Examples

Example 1: Find the GCF of 4 and 10, if their LCM is 20. Solution:

∵ LCM × GCF = 4 × 10

⇒ GCF(4, 10) = (4 × 10)/20 = 2

Therefore, the greatest common factor of 4 and 10 is 2.

Example 2: The product of two numbers is 40. If their GCF is 2, what is their LCM? Solution:

Given: GCF = 2 and product of numbers = 40

∵ LCM × GCF = product of numbers

⇒ LCM = Product/GCF = 40/2

Therefore, the LCM is 20.

Example 3: Find the greatest number that divides 4 and 10 exactly. Solution:

The greatest number that divides 4 and 10 exactly is their greatest common factor, i.e. GCF of 4 and 10.

⇒ Factors of 4 and 10:

Factors of 4 = 1, 2, 4

Factors of 10 = 1, 2, 5, 10

Therefore, the GCF of 4 and 10 is 2.

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## FAQs on GCF of 4 and 10

### What is the GCF of 4 and 10?

The . To calculate the greatest common factor (GCF) of 4 and 10, we need to factor each number (factors of 4 = 1, 2, 4; factors of 10 = 1, 2, 5, 10) and choose the greatest factor that exactly divides both 4 and 10, i.e., 2.

### How to Find the GCF of 4 and 10 by Prime Factorization?

To find the GCF of 4 and 10, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 10 = 2 × 5.

⇒ Since 2 is the only common prime factor of 4 and 10. Hence, GCF (4, 10) = 2.

☛ Prime Numbers

### If the GCF of 10 and 4 is 2, Find its LCM.

GCF(10, 4) × LCM(10, 4) = 10 × 4

Since the GCF of 10 and 4 = 2

⇒ 2 × LCM(10, 4) = 40

Therefore, LCM = 20

☛ Greatest Common Factor Calculator

### How to Find the GCF of 4 and 10 by Long Division Method?

To find the GCF of 4, 10 using long division method, 10 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

### What are the Methods to Find GCF of 4 and 10?

There are three commonly used methods to find the GCF of 4 and 10.

By Prime Factorization

By Euclidean Algorithm

By Long Division

### What is the Relation Between LCM and GCF of 4, 10?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 4 and 10, i.e. GCF × LCM = 4 × 10.

GCF and LCM

GCF and LCM Worksheet

GCF and LCM Worksheet

Source : www.cuemath.com

## Greatest Common Factor of 4 and 10 GCF(4,10)

GCF of 4 and 10, find the biggest number that can divide two integers, learn what is the greatest common factor of 4 and 10.

Home » GCF Calculator

## What is the Greatest Common Factor of 4 and 10?

Greatest common factor (GCF) of 4 and 10 is 2.

GCF(4,10) = 2

We will now calculate the prime factors of 4 and 10, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4 and 10.

## How to find the GCF of 4 and 10?

We will first find the prime factorization of 4 and 10. After we will calculate the factors of 4 and 10 and find the biggest common factor number .

### Step-1: Prime Factorization of 4

Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:

4 = 22

### Step-2: Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 21 × 51

### Step-3: Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1, 2

### Step-4: Factors of 10

List of positive integer factors of 10 that divides 4 without a remainder.

1, 2, 5

### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4 and 10. The biggest common factor number is the GCF number.

So the greatest common factor 4 and 10 is 2.

Also check out the Least Common Multiple of 4 and 10

### Related Greatest Common Factors of 4

GCF of 4 and 8 GCF of 4 and 9 GCF of 4 and 10 GCF of 4 and 11 GCF of 4 and 12 GCF of 4 and 13 GCF of 4 and 14 GCF of 4 and 15 GCF of 4 and 16 GCF of 4 and 17 GCF of 4 and 18 GCF of 4 and 19 GCF of 4 and 20 GCF of 4 and 21 GCF of 4 and 22 GCF of 4 and 23 GCF of 4 and 24

### Related Greatest Common Factors of 10

GCF of 10 and 14 GCF of 10 and 15 GCF of 10 and 16 GCF of 10 and 17 GCF of 10 and 18 GCF of 10 and 19 GCF of 10 and 20 GCF of 10 and 21 GCF of 10 and 22 GCF of 10 and 23 GCF of 10 and 24 GCF of 10 and 25 GCF of 10 and 26 GCF of 10 and 27 GCF of 10 and 28 GCF of 10 and 29 GCF of 10 and 30

Source : www.gcflcm.com

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James 17 day ago

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