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High School Algebra I: Help and Review25 chapters | 292 lessons

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Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you'll learn what composite numbers are and briefly touch on prime numbers. You'll also learn a couple of rules about composite numbers. Then, you can test your new knowledge with a brief quiz.

Mr. Wallace is helping his son's class with a bake sale by taking the morning shift at the table. Altogether, the class's parents have brought six pies to sell. Mr. Wallace has a thing about rectangles, so he wants to arrange all the pies in a rectangular fashion. There are a couple of ways he could do this. He could set up one row of six pies or he could set up two rows of three pies each.

After the first rush of customers, Mr. Wallace has a mess of three pies. He's going to arrange them in a rectangular fashion again, but he only has one way to do it now: one row of three pies. Of course, he could arrange the line of pies vertically rather than horizontally, but he'd still have just one row of three pies.

When Mr. Wallace arranges the three pies, he's creating a model of multiplication. Three rows of one item is like writing 3 x 1, which gives us a product of 3. But that was the only way Mr. Wallace had of arranging those three pies because 1 and 3 are the only numbers that we can multiply together to get a factor of 3. In other words, 1 and 3 are its only **factors**, or numbers you multiply together to get a certain product.

That makes 3 a **prime number**, which is a number that has only two factors: 1 and itself. Because 3 has only two factors, there was only one way Mr. Wallace could arrange the 3 pies. There were two ways Mr. Wallace could arrange six pies, though. That's because there are two pairs of factors that we can multiply together to get a product of 6: 1 x 6 and 2 x 3. So, 6 has four factors: 1, 2, 3, and 6.

Because 6 has four factors, it's a **composite number**, which is a number that has more than two factors. In other words, a composite number is the opposite of a prime number.

After that first rush of customers, a parent showed up late bringing seven more pies. So Mr. Wallace is back up to ten pies. How could he arrange them into a rectangle? He could have one row of ten pies or he could have two rows with five pies each.

He can arrange ten pies in two ways because there are two factor pairs that give a product of 10. So, the factors of 10 are 1, 2, 5, and 10. Ten is a composite number because it has more than two factors.

If Mr. Wallace had an even number of pies, he could always make two rows of pies because 2 and another number are always one factor pair for even numbers.

For example, 2 x 4 is a factor pair of 8. So is 1 x 8, so 8 is composite.

2 x 5 is a factor pair of 10. So is 1 x 10, so 10 is composite.

2 x 6 is a factor pair of 12. So are 1 x 12 and 3 x 4, so 12 is composite.

And so on. . .

That makes nearly every even number composite because they have 1, 2, and at least two other numbers as factors. Two is the exception to this rule because its only factors are 1 and 2. It's too small to take advantage of this rule. But every even number larger than 2 is always composite.

Similarly, nearly any number ending in 5 or 0 is divisible by 5 and is therefore composite.

For example, 3 x 5 is a factor pair of 15. So is 1 x 15, so 15 is composite.

4 x 5 is a factor pair of 20. So is 1 x 20 and 2 x 10, so 20 is composite.

And so on. . .

That makes nearly every number ending in 5 or 0 composite because they have 1, 5, and at least two other numbers as factors. Five is the exception to this rule because its only factors are 1 and 5. It's too small to take advantage of this rule. But every number larger than 5 that ends in 5 or 0 is always composite.

**Factors** are numbers you multiply together to get a certain product. A **prime number** is a number whose only factors are one and itself. A **composite number** is the opposite of a prime number; it has more than two factors. Even numbers larger than 2 are always composite. Numbers that end in 5 or 0 and that are larger than 5 are always composite.

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High School Algebra I: Help and Review25 chapters | 292 lessons

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
- The Order of Real Numbers: Inequalities 4:36
- Finding the Absolute Value of a Real Number 3:11
- What Are Composite Numbers? - Definition & Examples 4:38
- What are Real Numbers? - Definition & Properties 4:50
- What is Long Division? - Definition & Examples 3:29
- Go to High School Algebra - Real Numbers: Help and Review

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