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Math for Kids23 chapters | 325 lessons

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Instructor:
*Dina Albert*

When you use multiplication to find a total amount, you are working with factors. In this lesson, we will define what a factor is and explore real-world situations in which you work with factors to solve problems.

A **factor** is a number that you multiply with another number to get a product (the solution to a multiplication problem). Think of a multiplication problem as factors being multiplied to find the product. For instance, 2 and 4 are factors of 8:

A number can have just two factors or many, many factors. But how? Let's explore further.

Let's start by looking at numbers that have only two factors--for example, the number 2. How do you make 2 using multiplication? By multiplying 1 x 2 or 2 x 1. We can say that multiplying 2 and 1 is the only way to make a product of 2. And so, we can also say that 2 has only two factors: 1 and 2.

What about the number 3, how many factors does 3 have? Let's restate the question and ask: What numbers can we multiply together to make a product of 3? Well, the only way to make 3 is by multiplying 1 x 3 or 3 x 1. So, we can say that 3 has only two factors: 1 and 3.

One more example of a number with only two factors is 5. Why? Because we can only make 5 by multiplying 1 x 5 and 5 x 1. So, 5 only has two factors: 1 and 5.

Notice that all three of the numbers we discussed above had factors of 1 and itself.

- 5 had factors of itself (5) and 1
- 3 had factors of itself (3) and 1
- 2 had factors of itself (2) and 1

Numbers such as 2, 3, 5--and any other number that only has factors of itself and 1--are called **prime numbers**.

Now that we have discussed numbers with only two factors, let's take a look at some numbers that have more than two factors. Numbers that have more than two factors are called **composite numbers**. Since we skipped the number 4 in our last examples, that's the number we'll start with. This time we will use a multiplication chart to find all the ways we can make 4.

Notice that, in the chart, the 4 is highlighted in yellow. Those 4s (and, in fact, all the numbers inside the chart) are the products. The numbers at the top and on the side that are highlighted in red are the factors. To make 4, we have two different sets of factors to choose from: 2 x 2 = 4 and 4 x 1 = 4. So, the factors of 4 are: 1, 2, and 4.

Now let's look at the number 6 inside the chart, and find all the factors highlighted in red that can be multiplied together to make 6. To make 6, we can choose from two different sets of factors: 2 x 3 and 1 x 6. So, the factors of 6 are: 1, 2, 3 and 6.

When we multiply numbers to get a final answer, the numbers we use are called **factors**. A factor is a number that we multiply by another number to get a product (answer).

- Remember: factor x factor = product.

Some numbers have only two factors and are called **prime numbers**. If a number has more than two factors, it is called a **composite number**.

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Math for Kids23 chapters | 325 lessons

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