GCF of two or more Numbers Calculator: The Greatest Common Factor (GCF) Calculator is used to calculate GCF of two or more whole numbers. Here, you can enter numbers separated by a comma “,” and then press the Calculate button to get the GCF of those numbers.

Greatest Common Factor (GCF) Calculator is the most excellent handy calculator for calculating GCF!

## Greatest Common Factor (GCF) Calculator f0r two or more Numbers

### What is a Factor?

Factors are the numbers that we can multiply to each other to get one different number like 4 x 5 = 20, here 4 and 5 are factors

It is also possible to have various factors of a number like

4 x 5 = 20, 2 x 10 = 20, 1 x 20 = 20

Factors of 20: 1, 2, 4, 5, 10, and 20

### What is a Common Factor?

So when we are finding the factors of two numbers like

Factors of 12 of 1, 2, 3, 4, 6, and 12

Factors of 20 of 1, 2, 4, 5, 10, and 20

So here common factors are 1, 2, and 4

A common factor is a factor of two or more numbers.

### What is the Greatest Common Factor (GCF)?

Greatest Common Factor is just the biggest of the common factors. We can define it as:

The GCF is the greatest positive whole number from the set of a number that divides equally into all numbers with zero remainders.

So here if we are taking the previous example, then the Greatest Common Factor of 12 and 20 is 4.

Then, What is the Greatest Common Factor of 0?

We know that when we multiply any whole number to zero, it becomes zero so it is clear that each non zero whole number is a factor of 0. Like

n × 0 = 0 so, 0 ÷ n = 0, where n is any whole number

So GCF(n,0) = n, where n is any whole number

But, GCF(0, 0) is undefined.

### How to Get the Greatest Common Factor (GCF) of Any Numbers?

There are so many ways available to find out the greatest common factor of any whole numbers such as Factoring, Prime Factorization, Euclid’s Algorithm, and many more. Which one of the methods is useful for you is decided by some factors like

- How many numbers are there?
- How long are the numbers?
- What is the purpose of finding the GCF?

So, go for any of the methods and get your GCF. Let’s go through each method in detail.

#### 1.Factoring

Here, to check the Greatest Common Factor using the factoring method, we have to find out all the factors of each number manually or you can use any online Factors calculators also. So check out all the positive whole number factors of a number that can divide equally into the integers with zero remainders. Now write down all the common factors for each number, then find the biggest common number, it the GCF of numbers.

For detailed information see our **Factoring Calculator**.

Let’s check this with some examples to make it more simple,

Example 1:

Factors of 16: 1, 2, 4, 8, and 16

Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24

The common factor of 16 and 24: 1, 2, 4, and 8

The greatest common factor of 16 and 24: 8.

Example 2:

Factors of 15: 1, 3, 5, and 15

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 105: 1, 3, 5, 7, 15, 21, 35 and 105

Common factors of 15, 30 and 105: 1, 3, 5 and 15

Greatest Common Factor of 15, 30, and 105: 15.

#### 2. Prime Factorization

Prime Factorization is helpful when numbers are larger. If you want to calculate the Greatest Common Factor using prime factorization, then you have to check out all of the prime factors of each number manually or you can check it with an online Prime Factors Calculator. Now from the prime factors, list out all the common prime factors of the numbers. Find out the maximum same numbers from each prime factor and multiply them to find out the Greatest Common Factor.

For detailed information see our **Prime Factorisation Calculator**.

**Example 1: Find out GCF of 16 and 24?**

Prime Factorization of 16 = 2 x 2 x 2 x 2

Prime Factorization of 24 = 2 x 2 x 2 x 3

The occurrence of common prime factor of 16 and 24: 2, 2 and 2

The greatest common factor of 16 and 24 is 2 x 2 x 2 = 8.

**Example 2: Find out GCF of 15, 30 and 105**

Prime factorization of 15 = 3 x 5

Prime factorization of 30 = 2 x 3 x 5

Prime factorization of 105 = 3 x 5 x 7

Common factors of 15, 30 and 105 = 3 and 5

Greatest Common Factor of 15, 30, and 105 = 3 x 5 = 15

#### 3. Euclid’s Algorithm

Now, what if we are required to check the greatest common factor of very large numbers like 134334, 124456, or 187644? Some online calculators like Greatest Common Factor (GCF) or Factoring Calculator can help to find out the GCF of such a large number but what if you need to do it manually by yourself.

Step by step procedure to find the GCF of larger numbers with the help of Euclid’s Algorithm

- From the given numbers, first of all, take 2 whole numbers, and from the big number subtract the smaller number and write the result.
- Now subtract the small number from the result. Do it again and again till the result is less than the original small number.
- Now use the small number as a larger number and subtract the result you got from step two. Repeat the same procedure for every new bigger number and smaller number till you get the 0.
- Now if you get 0, then go back to one step before you get 0, the greatest common factor is the number you got just before the 0.

For detailed information see our **Euclid’s Algorithm Calculator**.

Let’s check it out with some examples.

**Example 1: Find out GCF of 16 and 24**

24 – 16 = 8

16 – 8 – 8 = 0

So, the GCF of 16 and 24 is 8, the least result we had before we got zero.

**Example 2: Find out GCF of 15, 25 and 105**

Here we have 3 numbers and for this, the method of finding GCF is:

GCF (x,y,z) = GCF (GCF (x,y),z)

So here we have to, first of all, find the greatest finding factor of 2 numbers and then we use its result with the 3rd number and find the GCF.

So Let’s get GCF (105, 25) first here,

105 – 25 = 80

80 – 25 = 55

55 – 25 = 30

30 – 25 = 5

25 – 5 = 20

20 – 5 – 5 – 5- 5 = 0

So, the greatest common factor of 105 and 25 is 5.

Now let’s check GCF of 3rd number, 15, and our result is also 5, GCF (5, 15)

15 – 5 – 5 – 5 = 0

So, the GCF of 15 and 5 is 5.

Therefore, the greatest common factor of 105, 25, and 15 is 5.

**Example 3: Find the GCF 268442, 178296, and 66888**

First of all, let’s find the GCF (268442, 178296)

268442 – 178296 = 90146

178296 – 90146 = 88150

90146 – 88150 = 1996

88150 – (1996 x 44) = 326

1996 – (326 x 6) = 40

326 – (40 x 8) = 6

40 – (6 x 6) = 4

6 – 4 = 2

4 – (2 x 2) =

So, the greatest common factor of 268442 and 178296 is 2.

Now we check the GCF (2, 66888)

66888 – (2 x 33444) = 0

So, the GCF of 2 and 66888: 2.

Hence, the GCF of 1268442, 178296, and 66888 is 2