# Common Factors – Definition, GCF, Examples, Facts

Updated on January 4, 2024

At Brighterly, we are committed to shining a light on the fascinating world of mathematics, illuminating the way for young learners. Today, we are diving into the magical universe of Common Factors. These magical keys can unlock the doors to a better understanding of numbers and their relationships. They are the friends who help us share our birthday cake equally, ensuring everyone gets a slice, and nobody is left out. With common factors, we can solve everyday mathematical problems more easily, whether it’s figuring out how many apples to divide among friends, or splitting chores equally in the family. So, let’s embark on this exciting journey of discovery and learn more about common factors, including their definition, the method of finding the Greatest Common Factor (GCF), examples, and interesting facts. Get ready to light up your math world, Brighterly style!

## What are Common Factors?

Common factors, also known as common divisors, are numbers that divide exactly into two or more other numbers. These little number magicians help us break down big, scary numbers into more manageable parts. They’re like the good friends who help us share out our birthday cake fairly, ensuring that everyone gets an equal piece and no one is left out.

Imagine you have two numbers, let’s say 12 and 18. A common factor of these two numbers is a number that divides both of them without leaving a remainder. In this case, numbers such as 1, 2, 3, and 6 can be used to evenly divide both 12 and 18 – making these our common factors.

## How to Find Common Factors?

Learning how to find common factors can be as exciting as embarking on a treasure hunt! Firstly, identify all the factors of each number. A factor is simply any number that divides into another number exactly. For example, the factors of 10 are 1, 2, 5, and 10, because these numbers can all be multiplied together to give us the number 10. Once we have our factors, we compare the two lists and look for the numbers that appear in both – these are our common factors.

## Common Factors of Two Numbers

Let’s take two numbers as examples – 15 and 25.

The factors of 15 are 1, 3, 5, and 15. The factors of 25 are 1, 5, and 25.

If we look at both lists, we can see that the numbers 1 and 5 appear in both lists, making them our common factors of 15 and 25.

## Common Factors of 12 and 18

So, what about the common factors of 12 and 18?

The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18.

Our common factors here are 1, 2, 3, and 6.

## Common Factors of 8 and 24

And how about the common factors of 8 and 24?

The factors of 8 are 1, 2, 4, and 8. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

This means that the common factors of 8 and 24 are 1, 2, 4, and 8.

## What is the Greatest Common Factor?

The Greatest Common Factor (GCF) is the largest number that divides exactly into two or more numbers. In simple terms, it’s the biggest piece of birthday cake that we can fairly share between our friends. It’s like the team captain, the biggest and best of all the common factors.

For example, for our numbers 8 and 24, the common factors were 1, 2, 4, and 8. Of these, 8 is the largest – making it our Greatest Common Factor.

## Common Factors Examples

Now that we understand how to find common factors, let’s explore a few more examples:

- The common factors of 20 and 30 are 1, 2, 5, and 10.
- The common factors of 7 and 14 are 1 and 7.
- The common factors of 6 and 9 are 1, 2, and 3.

## Practice Questions on Common Factors

Time to put your newfound skills to the test with some practice questions:

- What are the common factors of 10 and 20?
- What are the common factors of 6 and 15?
- What are the common factors of 8 and 16?

## Conclusion

As we wrap up this enlightening journey into the world of common factors, we at Brighterly hope that we have been able to add some brightness to your mathematical understanding. By recognizing and understanding common factors, you now hold the keys to unlock various mathematical doors. These doors lead to understanding more complex concepts such as fractions, ratios, and algebra.

Remember, mathematics is not about rote learning, but understanding the relationships and patterns that numbers present us. And in this journey of numbers, know that Brighterly is always here, ready to guide and illuminate your path. So keep exploring, keep discovering, and most importantly, keep making your math world a little brighter!

## Frequently Asked Questions on Common Factors

### What is a common factor?

A common factor, also known as a common divisor, is a number that can divide two or more numbers without leaving a remainder. They are the numbers that can be multiplied to give us the original number. Common factors are like puzzle pieces that perfectly fit together to create the original picture, in this case, the original number.

### How do we find common factors?

To find common factors, we first need to list all the factors of each number. Once we have these lists, we can compare them and find the numbers that appear in both. These numbers are the common factors. Remember, it’s like looking for shared interests among friends – we are looking for the numbers that ‘interest’ or factor into both of our original numbers.

### What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF) is the largest number that can divide two or more numbers exactly. It’s the biggest piece of the mathematical cake that can be shared between our numbers. The GCF is a valuable tool in many areas of mathematics, including simplifying fractions and solving algebraic problems.

### How to find the GCF?

To find the GCF, we start by finding all the common factors of the numbers. From this list of common factors, we identify the largest number. This number is our Greatest Common Factor.