# How to Find the Greatest Common Factor (GCF)

In this post, you learn how to find the Greatest Common Factor (GCF) of two or more numbers using a few simple and easy steps.

## Step by step guide to finding the Greatest Common Factor

• List the prime factors of each number.
• Multiply common prime factors.
• If there are no common prime factors, the GCF (Greatest Common Factor) is $$1$$.

### Greatest Common Factor – Example 1:

Find the GCF for $$8$$ and $$12$$.

Solution:

The factors of $$8$$ are: $$\{1, 2, 4, 8\}$$
The factors of $$12$$ are: $$\{1,2,3,4,6,12\}$$
Number $$4$$ is in both factors.
Then the greatest common factor is: $$4$$.

### Greatest Common Factor – Example 2:

Find the GCF for $$14$$ and $$18$$.

Solution:

The factors of $$14$$ are: $$\{1,2,7,14\}$$
The factors of $$18$$ are: $$\{1,2,3,6,9,18\}$$
There is $$2$$ in common
Then the greatest common factor is: $$2$$.

### Greatest Common Factor – Example 3:

Find the GCF for $$10$$ and $$15$$ and $$25$$ .

Solution:

The factors of $$10$$ are: $$\{1,2,5,10\}$$
The factors of $$15$$ are: $$\{1,3,5,15\}$$
The factors of $$12$$ are: $$\{1,5,25\}$$
Factor $$5$$ is in common.
Then the greatest common factor is: $$5$$.

### Greatest Common Factor – Example 4:

Find the GCF for $$8$$ and $$20$$.

Solution:

The factors of $$8$$ are: $$\{1,2,4,8\}$$
The factors of $$20$$ are: $$\{1,2,4,5,10,20\}$$
Numbers $$2$$ and $$4$$ are in common.
Then the greatest common factor is: $$4$$.

## Exercises for practicing the Greatest Common Factor

### Find the GCF for each number pair.

1. $$\color{blue}{20, 30}$$
2. $$\color{blue}{4, 14}$$
3. $$\color{blue}{5, 45}$$
4. $$\color{blue}{68, 12}$$
5. $$\color{blue}{5, 6, 12}$$
6. $$\color{blue}{15, 27, 33}$$

1. $$\color{blue}{10}$$
2. $$\color{blue}{2}$$
3. $$\color{blue}{5}$$
4. $$\color{blue}{4}$$
5. $$\color{blue}{1}$$
6. $$\color{blue}{3}$$

## Related to "How to Find the Greatest Common Factor (GCF)"

1. Savannah says:

The greatest common factor for 8 and 20 is 4. The text multiplies 2 and 4 to find 8 but since 8 does not factor into 20 that cannot be correct.

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