# What is the Highest Common Factor (HCF)?

The steps to finding the Highest Common Factor are hidden in its name. Can you guess what they are? Let’s find out together!

Author
Amber Watkins

Published
July 2024

# What is the Highest Common Factor (HCF)?

The steps to finding the Highest Common Factor are hidden in its name. Can you guess what they are? Let’s find out together!

Author
Amber Watkins

Published
July 2024

# What is the Highest Common Factor (HCF)?

The steps to finding the Highest Common Factor are hidden in its name. Can you guess what they are? Let’s find out together!

Author
Amber Watkins

Published
July 2024

Key takeaways

• One of the most important reasons to learn how to find the highest common factors in maths is to use it to reduce fractions.
• How to find the Highest Common Factor, also known as the Great Common Divisor, can be easily remembered by writing its name backward. The steps are find the factors, choose the ones that are common, and select the highest.
• Using an online maths app can help your child get the needed practice finding the HCF.

There are a few times in maths that we get to work backward. When we do it is always fun! What are we solving? Problems with Highest Common Factors. You will sometimes see it called the HCF.

## What is the Highest Common Factor / Greatest Common Divisor?

As the name suggests, it involves three steps:

Step 1: Identifying the Factors of two numbers.
Step 2: Discovering which factors are Common.
Step 3: Comparing the Common factors to see which one is the Highest in value.

If you read those highlighted words starting with Step 3 backward to Step 1, what does it say? You guessed it: Highest Common Factors!

The Highest Common Factor definition says when comparing the factors two numbers have in common there will be one factor that is also the highest in value. This number is called the highest common factor, or the greatest common divisor.

Let’s break it down step-by step!

## What are Factors?

Factors are the numbers you multiply to get an answer. For example, what are the factors of 12?

To get 12, you can multiply 1 x 12, 2 x 6, or 3 x 4. So those numbers would be factors of 12.

Question: What are the factors of 12?
Answer: The factors of 12 are the numbers 1, 2, 3, 4, 6, and 12.

## What are Common Factors?

Common factors are factors that both numbers share. You will find the same number in both lists of factors. For example, the factors for 6 are 1 , 2, 3 and 6. The factors for 12 are the numbers 1, 2, 3, 4, 6, and 12.

Question: What are the Common factors of 6 and 12?

Answer: Since both numbers have 1, 2, 3, and 6 as factors, they are the common factors.

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## How to Find the Highest Common Factor

Begin by writing Highest Common Factor on your paper backward. It should look like this:

1. Factors
2. Common
3. Highest

Now we have the steps of how to find the highest common factor

First, find the factors of the two numbers.

Next, circle the factors that both lists have in common.

Finally, select the factor that is the highest in value.

Let’s listen in to the following conversation as a teacher explains how to find the highest common factor of 10 and 15 for one of her students.

Teacher: “Today we will find the highest common factor of 10 and 15. On your paper can you list all of the factors of 10?”

Student: “Yes, 1 x 10 equals 10 and 2 x 5 equals 10.

So, 1, 2, 5, and 10 are all the factors of 10.”

Teacher: “Perfect, and what about 15, what are the factors of 15?”

Student: “1 x 15 and 3 x 5. So 1, 3, 5, and 15 are factors of 15.”

Teacher: “In those two lists do you see any numbers in common?”

Student:  “Yes, 1 and 5.”

Teacher: “So looking at both numbers, which do you think is the Highest common factor?”

Student:  “5.”

You can see how easy it is to find the HCF as long as you follow those three steps.

## HCF Practice Problems

What is the highest common factor (HCF) of 18 and 24?

What is the highest common factor (HCF) of 48 and 36?

What is the greatest common divisor (GCD) of 16 and 12?

## FAQs About Highest Common Factors

HCF stands for highest common factor. The highest common factor is the factor that is common to two numbers that is also the greatest in value.

You find the highest common factor by finding the factors of two numbers, then comparing the factors to find which are common to both, finally you select the factor that is the greatest or highest in value.

HCF is a comparison of factors, or numbers that are multiplied to get an answer. LCM is a comparison of multiples, or the answers you get when counting by a number. HCF is finding the highest factor, but LCM is finding the smallest multiple.

6 is the GCF.

1. First find the factors of 18: 1 x 18, 2 x 8, and 3 x 6.
2. Second order them from least to greatest 1, 2, 3, 6, and 18.
3. Next, find the factors of 24: 1 x 24, 2 x 12, 3 x 8, 4 x 6.
4. Order them from least to greatest: 1, 2, 3, 4, 6, 12, and 24
5. Next circle the factors from both lists that are found in both: 1, 2, 3, and 6
6. Finally, out of the factors you circled, which number is the greatest? 6

12 is the GCF

1. First find the factors of 48: 1 x 48, 2 x 24, 3 x 16, and 4 x 12, and 6 x 8.
2. Second order them from least to greatest: 1, 2, 3, 4, 6, 8, 12, 24, and 48.
3. Next, find the factors of 36: 1 x 36, 2 x 18, 3 x 12, 6 x 6, 4 x 9.
4. Order them from least to greatest: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
5. Next circle the factors from both lists that are found in both: 1, 2, 3, 4, 6, and 12.
6. Finally, out of the factors you circled, which number is the greatest? 12.

4 is the GCF.

1. First find the factors of 16: 1 x 16, 2 x 8, 4 x 4.
2. Second order them from least to greatest 1, 2, 4, 8, and 16.
3. Next, find the factors of 12: 1 x 12, 2 x 6, 3 x 4.
4. Order them from least to greatest: 1, 2, 3, 4, and 12.
5. Next circle the factors from both lists that are found in both: 1, 2, 4.
6. Finally, out of the factors you circled, which number is the greatest? 4.

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring primary through university level maths. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring primary through university level maths. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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