# Find the Greatest Common Factor (GCF) by Using Factor Trees

Finding the greatest common factor, otherwise known as the GCF, for a set of large numbers can be quite a daunting task. It can be really difficult to think of all the factors for large numbers.

Lucky for us, prime factorization, otherwise known as "factor trees" was discovered. Factor Trees allow us to write the product as a series of prime factors. By writing the prime factorization, we can then easily find the GCF for two large numbers pretty easily.

Here are the steps and then we will take a look at an example.

## Steps for Finding the GCF Using Factor Trees

### Step 1: Write the prime factorization for each number. It may be easier to write it in extended form, not with exponents.

### Step 2: Circle the common factors.

### Step 3: Multiply the common factors together and this is the GCF!

## Finding the GCF Using Factor Trees for 360 and 540

Factor trees (or prime factorization) can be an easy way to find the greatest common factor for two large numbers. Simply find all of the prime factors and identify the common factors. Multiply your common factors together and you end up with the greatest common factor for both numbers!

Now that you know two ways to find the greatest common factor of two numbers, you are ready for the next lesson on equivalent fractions.

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