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# What Is A Factor?

As we begin our study of fractions, we need to have a clear understanding of factors. So, what is a factor?

## Definition: **Factor**

### A **factor** is a number that divides into another number without a remainder.

So, for example, 5 is a factor of 20 because 20/5 = 4. There is no remainder.

You can also think of factors as the numbers that you multiply together in order to obtain a product. For example, 4 and 5 are factors of 20 because 4(5) = 20.

Many numbers, like 20, have a lot of different factors. You may need to think of all of the different factors for a number when working with fractions.

Let's take a look at Example 1, where we will list all of the factors for a particular number.

## Example 1 - Identifying Factors

As you can see from Example 1, when asked to find factors, simply think of the whole numbers that you multipy together in order to obtain the product. Yes, this is where knowing those multiplication facts really comes in handy!

As you begin to compare two numbers, you may be asked to find common factors. When thinking of the word *common*, how would you define **common factors**?

## Definition: **Common Factors**

**Common Factors** are the factors that are the same for a set of numbers. First you must find all of the factors and then identify the "common" factors.

## Example 2 - Common Factors

Common factors are simply the factors that are the same for two or more numbers. Not too hard, right?

As we continue our study of factors, we will take a look at the greatest common factor and using factor trees to help identify the greatest common factor. However, we will first study prime and composite numbers in the next lesson.

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