GCF calculator is a free online tool that allows you to find the Greatest Common Factor of a given set of numbers.

Welcome to our GCF Calculator. It calculates the Greatest Common Factor (GCF) of two or more numbers. Just input the numbers for which you want to find the GCF and get the instant result on your screen. Also, our tool shows the Least Common Multiple (LCM) result too. Mostly, it is used in mathematical operations like simplifying fractions, finding common denominators, or solving equations involving multiple variables.

- Firstly, enter the positive integer numbers into the input box.
- Make sure to separate each number using comma or space. For example, 12, 15, 28 or 30 25 56.
- Now click on the Calculate button to get GCF and LCM result.
- Lastly, press the Reset button for new GCF calculation.

The Greatest Common Factor (GCF) is the largest number that divides two or more non-zero numbers without a remainder. It's the highest number in all common factors of two or more numbers. Also, It's known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF).

GCF is denoted as:

GCF (a, b)

**Example:** GCF(45, 120) = 15

There are several methods to find GCF. Here we will discuss some of the most common methods.

In this method, firstly, we will list the factors of given numbers and find the gratest number in all common factors. Also, we can use the Factoring Calculator to find the factors of numbers.

Find the GCF of 10, 24, and 32.

Firstly, list all the factors of 10, 24, and 32.

10 = **1**, **2**, 5, 10

24 = **1**, **2**, 3, 4, 6, 8, 12, 24

32 = **1**, **2**, 4, 8, 16, 32

Now find the highest common factor. That is 2.

So, **GCF(10, 24, 32) = 2**.

In the prime factorization method, we will list the prime factors of all numbers. Then, multiply all common factors to get the GCF.

Find the GCF of 36, 48, and 52.

Firstly, find the prime factors of all numbers.

36 = **2** × **2** × 3 × 3

48 = **2** × **2** × 2 × 2 × 3

52 = **2** × **2** × 13

Now multiply the common factors. That is 2 × 2 = 4.

So, **GCF(36, 48, 52) = 4**.

Prime factorization method is only used for small integer numbers. Because it becomes very difficult to determine the common factors for larger numbers. For larger numebers, Euclidean Algorithm method is more convenient.

This method is specially used to find the GCF for very large numbers like 23668, 45856, and 7455878.

The algorithm is as below:

- GCF(x, x) = x
- GCF(x, y) = GCF(x-y, y), when x > y
- GCF(x, y) = GCF(x, y-x), when y > x

Let's take an example.

Find the GCF(644896, 345782).

GCF(644896, 345782)

644896 - (345782 × 1 R) = 299114

345782 - (299114 × 1 R) = 46668

299114 - (46668 × 6 R) = 19106

46668 - (19106 × 2 R) = 8456

19106 - (8456 × 2 R) = 2194

8456 - (2194 × 3 R) = 1874

2194 - (1874 × 1 R) = 320

1874 - (320 × 5 R) = 274

320 - (274 × 1 R) = 46

274 - (46 × 5 R) = 44

46 - (44 × 1 R) = 2

44 - (2 × 22 R) = 0

Here, R = Remainder.

So, the greatest common factor of 644896 and 345782 is **2**.

As you can see, all methods work differently and it's difficult to calculate the GCF manually using these methods. So, it's better to use our GCF Calculator to make it easier and faster.