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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to factor any whole number that you are given. You will learn what factors are and how a whole number can have several different factors.

In this video lesson, we talk about **whole numbers**. These are your counting numbers plus 0. When we count, we begin with 1, 2, then 3 and so on. But with whole numbers, we begin with 0. So we have 0, 1, 2, 3, and so on. They are called whole numbers because they don't have a decimal.

You can also think of whole numbers as numbers that can represent a number of items. For example, we usually say that we saw 6 red cars pass by. We usually won't say that we saw 2.5 cars - unless there was an accident or something went wrong!

Now, **factors** are numbers that multiply together to get another number. When we multiply any two or more numbers together, we are multiplying factors together. You can think of factors as simply the numbers used in multiplication.

As you can see, any number can be a factor because you can multiply any number by any other number. For example, the numbers 2 and 3 are factors in 2 * 3 = 6. When multiplied together, they give you 6. So we say that 2 and 3 are factors of 6. If you think about it, 1 and 6 are also factors of 6 because we can multiply 1 * 6 to get 6. You can think of factors as pieces that make our number, like building blocks that together make one building.

We can ask the question, 'How do we find what our factors are?' How can we break apart our number into its building blocks, into its pieces? This is something that you will need to know for your tests and as you progress in your lessons.

Since we know that our factors are the numbers that multiply together to get our number, we can use what we know of the multiplication table to find our factors. For the number 6 that we mentioned, we know that 2 times 3 equals 6 as does 1 times 6. The numbers 4 and 5 can't be multiplied with any other number to get 6. We knew this from our knowledge of the multiplication tables. Our factors are 1, 2, 3, and 6.

Otherwise, if we just manually started to divide our 6 by whole numbers starting with 1 and ending with our number, then we would also find our factors. Our factors would be the numbers we used to divide where the answer is another whole number. Performing our divisions we get 6 / 1 = 6, 6 / 2 = 3, 6 / 3 =2, 6 / 4 = 1.5, 6 / 5 = 1.2, and 6 / 6 = 1. What numbers give us another whole number as an answer? We have 1, 2, 3, and 6. So that means our factors are 1, 2, 3, and 6, the same as the ones we found by using our knowledge of the multiplication tables.

Let's look at another example.

*What are the factors of 10?*

Using what we know of the multiplication tables, we know that 2 * 5 equals 10 as does 1 * 10. Besides these, we don't have any other numbers. So our factors are 1, 2, 5, and 10.

If we wanted to make doubly sure of these factors, we could systematically divide our 10 by whole numbers starting from 1 and ending at 10. We get 10 / 1 = 10, 10 / 2 = 5, 10 / 3 = 3.33, 10 / 4 = 2.5, 10 / 5 = 2, 10 / 6 = 1.66, 10 / 7 = 1.42857, 10 / 8 = 1.25, 10 / 9 = 1.11, and 10 / 10 = 1. Looking at our divisions, we find that the only numbers that give us another whole number for an answer are 1, 2, 5, and 10. All the others give us a decimal answer and thus are not factors.

Let's review what we've learned.

**Whole numbers** are our counting numbers plus 0. **Factors** are numbers that multiply together to get another number. To find factors, we use either our knowledge of the multiplication table or by systematically dividing our number starting with 1 and ending with our number. Our factors, then, are the numbers we used to divide where the answer is another whole number.

By the time you are done with this lesson, you should be able to identify the factors of a whole number.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- What is Factoring in Algebra? - Definition & Example 5:32
- Equivalent Expressions and Fraction Notation 5:46
- Factoring Out Variables: Instructions & Examples 6:46
- Combining Numbers and Variables When Factoring 6:35
- Transforming Factoring Into A Division Problem 5:11
- Factoring By Grouping: Steps, Verification & Examples 7:46
- Finding Factors of Whole Numbers 5:16
- Go to 6th-8th Grade Math: Factoring

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