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

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

### 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: \(4\).

## Exercises

### Find the **GCF** for each number pair.

- \(\color{blue}{20, 30}\)
- \(\color{blue}{4, 14}\)
- \(\color{blue}{5, 45}\)
- \(\color{blue}{68, 12}\)
- \(\color{blue}{5, 6, 12}\)
- \(\color{blue}{15, 27, 33}\)

### Download Greatest Common Factor Worksheet

- \(\color{blue}{10}\)
- \(\color{blue}{2}\)
- \(\color{blue}{5}\)
- \(\color{blue}{4}\)
- \(\color{blue}{1}\)
- \(\color{blue}{3}\)

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.