Now we all know, that the greatest common factor is basically the highest number that can be divided into two numbers (or even more). To put it in simple words, in order to fin the greatest common factor of two numbers, you basically need to find the factors that are common between the two of them, and then see the greatest among those common factors. This particular factor is to be considered as being the greatest common factors of those two numbers (or more).

Now, although working out the GCF is extremely easy, students that are just starting out with them tend to find it a bit hard. For this reason, here are a few greatest common factor examples that are sure to help you understand them better. These examples of greatest common factor will make it extremely easy for you to gain better insight in to the determination of the GCF. Here they are:

## A few GCF examples for your help

### Example # 1:

Let us consider a very basic example at first. For this purpose, we will be finding the greatest common factor of 8, and 12. Here it is:

The factors of 8 are: 1, 2, 4, and 8

The factors of 12 are: 1, 2, 3, 4, 6, and 12.

Their common factors, as can be seen, are: 1, 2, and 4.

Hence, their greatest common factor, which is the largest common factor amidst the two, would be: 4.

### Example # 2:

Now, moving on, let us consider an example where we will be finding the GCF by means of prime factors. In this example, there is just one common factor. Here, we will be finding the greatest common factor of 14 and 49.

The prime factors of 14 are: 2 X 7

The prime factors of 49 are: 7 X 7

Now, considering that the only common factor is that of 7, the greatest common factor for 14, 49 will be 7.

### Example # 3:

Now let us find the greatest common factor of three numbers. The numbers that we will be working on are 15, 30 and 105.

The factors of 15 are: 1, 3, 5, and 15.

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.

The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, and 105.

Now, amid all the factors of the three numbers, the ones that are common are: 1, 3, 5, and 15.

Hence, the greatest common factor here is going to be 15 as it is the largest of the common factors of 15, 30, and 105.

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