# Greatest common factor definition: All that you should know about GCFs

Before getting into the **greatest common factor definition**, it is necessary for you to know what factors are. Well, by definition, factors are basically the numbers that are multiplied together in order to attain another number. For example:

Now, moving on, you should know what common factors are. For this purpose, consider an example. Work out the factors of 12 and 30. For 12, the factors would be: 1, 2, 3, 4, 6, and 12. On the other hand, the factors for 30 would be: 1, 2, 3, 5, 6, 10, 15, and 30. In both these lists, the common factors would be the numbers that appear ‘commonly’ in both the lists. In this case, the common factors of 12, and 30 would be: 1, 2, 3, and 6.

## Alright, but what is greatest common factor?

As per the most basic **GCF **definition, the largest of the common factors is basically referred to as the greatest common factor. For example, the common factors of 15 and 30 are 1, 3, 5, and 15, so that makes 15 the greatest common factor.

Finding the greatest common factor is extremely easy. What you basically need to do is basically take both numbers and find their factors. Once that is done, you would basically have to work out their common factors. Upon finding their common factors, you would have to choose the greatest number in all of them. See how easy it is to solve **greatest common factor problems**?

## Solving greatest common factor word problems

It is highly recommended for students who are just getting started with solving **GCF **to try to work out **greatest common factor word problems. **Start with the most basic ones and these are surely going to help you gain better insight into acquiring the **greatest common factor **of any number. There are two different means of finding the **GCF**. These are typically inclusive of comparing common factors to acquire these, and making use of common prime factors for the said purpose. Don’t be scared of working on these as once you start understanding **what is greatest common factor, **things would be a whole lot easier for you. ** **

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