Highest Common Factor Worksheets 38: Find the highest common factor (HCF) of each set of numbers. Click the button below to try all our FREE online, PDF, or printable Greatest Common Factor worksheets.

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What are factors?

The two numbers that we multiply together to get a multiple are called **factors**.

Factor x Factor = Multiple

**4 x 7 = 28**

What are common factors?

When you list the factors of two or more numbers (or multiples), sometimes you can see some factors are in all the lists of factors. These factors which appear in all the lists of factors are called **common factors**.

What is Highest Common Factor (HCF)?

The largest common factor of a list of common factors is called the **Highest Common Factor**. In short we call it **HCF**.

Highest common factor (HCF) is also known as the **Greatest Common Factor (GCM)**.

Follow the example below to find the highest common factor (HCF) or the greatest common factor (GCF) of a number pair.

**Find the highest common factor (HCF) of 24 and 32**

**Example 1:**

Step 1:

Find the factors of 24

**1**, **2**, 3, **4**, 6, **8**, 12, 24

Step 2:

Find the factors of 32

**1**, **2**, **4**, **8**, 16, 32

Step 3:

Group the common factors

**1, 2, 4, 8**

Step 4:

Find the highest factor of all the common factors

**8** is the highest factor of all the common factors of 24 and 32

Therefore 8 is the highest common factor of 24 and 32

**Example 2:**

Find the highest factor, which is common to both numbers that each number is divisible by.

This factor is the highest common factor of the number pair.

__24__

32

÷

÷

8

8

=

__3__

4

Therefore the highest common factor of 24 and 32 is 8.

**Finding the highest common factor of three numbers**

**Find the highest common factor (HCF) of 15, 30 and 105**

**Example:**

Step 1:

Find the factors of 15

**1**, **3**, **5**, **15**

Step 2:

Find the factors of 30

**1**, 2, **3**, **5**, 6, 10, **15**, 30

Step 3:

Find the factors of 105

**1**, **3**, **5**, 7, **15**, 21, 35, 105

Step 4:

Group the common factors

**1, 3, 5, 15**

Step 5:

Find the highest factor of all the common factors

**15** is the highest factor of all the common factors of 15, 30 and 105

Therefore 15 is the highest common factor of 15, 30 and 105.

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