# Greatest Common Factor

In this post, you learn how to find Greatest Common Factor of two or more numbers.

## Step by step guide to finding Greatest Common Factor

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

### 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: $$4$$.

### 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: $$2$$.

### 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: $$5$$.

### 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: $$2×4=8$$.

## Exercises

### 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. $$\color{blue}{3}$$