Common factors of numbers are factors that are common to both numbers. The Greatest Common Factor (GCF), as its name implies, is the greatest number between the common factors of two numbers. One of the most important uses of the Greatest Common Factor (GCF) is to simplify fractions.

## Related Topics

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

There are two ways to calculate the largest common factor:

**1- Use a list of factors to find the Greatest Common Factor (GCF)**

**Step 1:**To find the largest common factor between a set of numbers, list all the factors in each number.**Step 2:**Next, select the common factors.**Step 3:**Finally, the greatest factor in all lists is The Greatest Common Factor (GCF).

**2- Use the prime factorization to find the Greatest Common Factor (GCF)**

You can use prime factorization to find the Greatest Common Factor (GCF) for a set of numbers. In the case of bigger numbers – which are time-consuming to create a list of factors – this method usually works best.

**Step 1:**List the prime factors of each number.**Step 2:**Draw a circle around the prime factors that are common to all lists.**Step 3:**Multiply the numbers which you have drawn a circle around them. The answer is the Greatest Common Factor (GCF) between those numbers.

**Note:**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: \( \{1,2,3,4,6,12\} \)

Numbers \(2\) and \(4\) are in common.

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 \(25\) 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.

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

### Download Greatest Common Factor Worksheet

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

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Savannah–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.