Back To Course

Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide17 chapters | 166 lessons | 10 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you'll review factors and prime numbers. You'll learn what a factor tree is and see how it works to reveal any number's prime factorization. Then you can test your new knowledge with a brief quiz.

When we make a family tree, we make a chart of the people that came before us. They're called family trees because they tend to branch out as they progress, as each ancestor gives way to more ancestors. In the same way, a factor tree shows the numbers that come together to create a larger number, and it branches out as it progresses because each resulting factor then gives way to its own factors. In other words, a **factor tree** is a tool that breaks down any number into its prime factors.

Before we go into detail about factor trees, we need to review factors. **Factors** are simply numbers you can multiply together to get a certain product. For example, if we're looking at 2 * 3 = 6, then 2 and 3 are factors of 6. But, we could also say that 1 * 6 = 6. So 6 has four factors: 1, 2, 3, and 6. This factor business could get messy with large numbers because, generally speaking, the larger a number is the more factors it will have. That's where the factor tree comes in.

For an example of a factor tree, let's start with 100. We can split that number into any of its two factors. In other words, we're going to find two numbers that, when multiplied together, give us a product of 100. Let's start with 4 and 25 because 4 * 25 = 100. And, just like we would in a family tree, we're now going to find the 'ancestors,' or factors, of 4 and 25. We'll start with 4, which we could write as 2 * 2, so we'll put those factors into the tree under 4.

Now, if we were to break down 2 into its factors, we'd get 2 and 1. Then, we could break down 2 into 2 and 1 again. This could go on infinitely because 1 and 2 are 2's only factors. That makes 2 a **prime number**, a number whose only factors are 1 and itself. So instead of having an endless chain of twos and ones on the factor tree, we'll stop at 2. In relation to the factor tree, we call the prime numbers **prime factors** because when all of them are multiplied together they give the original number. We always stop a factor tree's branch at the prime factors to avoid an infinite chain of the same factors.

So we're done with 4's branches. Let's look at 25. We could write that number as 5 * 5, so we'll place those factors on the tree now. Just like 2, 5 is a prime number because its only factors are 1 and 5. Since it's a prime number, we'll end those branches. The factor tree doesn't necessarily produce all of a number's possible factors. For example, 10 is a factor of 100 (10 * 10), but it doesn't show up on the tree.

What the tree does give us is a number's prime factorization. A number's **prime factorization** is simply the list of prime numbers you would multiply together to get a certain product. On a factor tree, all the prime numbers at the ends of branches give us the prime factors. So 100's prime factorization is 2 * 2 * 5 * 5, or 2^2 * 5^2. Every number has one unique prime factorization, just like every person has one unique fingerprint.

Unlike a family tree, which is fixed and can only occur in one way, some factor trees have different possible arrangements. Let's reconsider 100's factor tree. We could have started with 10 * 10 because, just like 25 * 4, it also gives us a product of 100. Let's set up another factor tree for 100 using 10 and 10 as the first pair of factors.

Now, we'll break down 10. We could write 10 as 5 * 2, so those will be our next factors in the tree. And, since 2 and 5 are prime numbers, we'll end the branches there. Notice that even though we started with a different pair of factors for 100, we still end up at the same prime factorization: 2^2 * 5^2. No matter how we start a factor tree, if completed correctly, it will always reveal a number's prime factorization.

Now that we've seen a factor tree in action, let's challenge ourselves with a larger number. We'll use a factor tree to find the prime factorization of 2,310. Even though 2,310 is a much larger number than 100, we'll still follow the same steps to create its factor tree. In fact, we'll start with 231 and 10 as the first pair of factors.

We can write 231 as 77 * 3. We can also break 10 down into its factors, 2 and 5. Now we have the prime factors of 2, 3, and 5. But, we can still break 77 down into 7 * 11. Now, all our branches end in prime numbers. So 2,310's prime factorization is 2 * 3 * 5 * 7 * 11. We could have started this tree with any factor pair, such as 1,155 * 2 or 770 * 3. When we carried out the factor tree, we would still discover the same prime factorization.

**Factors**are the numbers you multiply together to get a certain product.- A
**prime number**is a number whose only factors are 1 and itself. - A
**factor tree**is a tool that breaks down any number into its prime factors. - A certain number's
**prime factorization**is the list of prime numbers or prime factors that you would multiply together to create that certain number. - No matter how you start a number's factor tree, it will always give you the one unique prime factorization for that number.

**Factor tree:** a tool that breaks down any number into its prime factors

**Factors:** numbers you can multiply together to get a certain product

**Prime number:** a number whose only factors are 1 and itself (also called prime factors)

**Prime factorization:** the list of prime numbers you would multiply together to get a certain product

Utilize this lesson's main points as you prepare to:

- Distinguish between factors and a factor tree
- Understand the process of splitting numbers
- Use a factor tree

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
10 in chapter 2 of the course:

Back To Course

Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide17 chapters | 166 lessons | 10 flashcard sets

- What is Factoring in Algebra? - Definition & Example 5:32
- How to Find the Prime Factorization of a Number 5:36
- Using Prime Factorizations to Find the Least Common Multiples 7:28
- Equivalent Expressions and Fraction Notation 5:46
- Using Fraction Notation: Addition, Subtraction, Multiplication & Division 6:12
- 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
- What is a Factor Tree? - Definition & Example 6:09
- Go to Factoring in Algebra

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Early Civilizations & The Ancient Near East
- Fundamental Overview of World War I
- The Virginia Dynasty & Jacksonian America
- 1920's America and the Great Depression
- Building the United States After the American Revolution
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Subtraction in Java: Method, Code & Examples
- Hydrogen Chloride vs. Hydrochloric Acid
- Extraction of Aluminum, Copper, Zinc & Iron
- Iroquois Culture, Traditions & Facts
- Noun Clauses Lesson Plan
- Adverb of Manner Lesson Plan
- Timeline Project Ideas for High School
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - What is a Diastereoisomer?
- Quiz & Worksheet - Mauryan Empire Art & Culture
- Quiz & Worksheet - What is a Convergent Sequence?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- ESL Conversation Questions & Topics for ESL Students
- Calculus Worksheets

- FTCE General Knowledge Test (GK) (827): Reading Subtest Practice & Study Guide
- Middle School US History: Tutoring Solution
- NY Regents Exam - Geometry: Tutoring Solution
- GMAT Prep: Help and Review
- Algebra I Textbook
- Overview of the US Constitution - MTEL Political Science/Political Philosophy
- Michigan Merit Exam - Math: Properties of Functions
- Quiz & Worksheet - Rules for Spelling Suffixes & Endings
- Quiz & Worksheet - Adversarial System of Justice Benefits
- Quiz & Worksheet - Ammonium Nitrate Uses & Formula
- Quiz & Worksheet - Practice Solving Combinations
- Quiz & Worksheet - Practice Multiplying 2-Digit Numbers

- Neoclassical Criminology: School & Theory
- Ancient Egyptian God Shu: Myth, Symbol & Facts
- How Much Does a Smart Board Cost?
- What is CCNA Certification?
- How to Pass the Earth Science Regents Exam
- Global History & Geography Regents Exam Info
- Math Fraction Games
- Florida Alternative Teacher Certification
- FTCE Biology 6-12: Passing Score
- History Books for Kids
- Learning Activities for Children with Down Syndrome
- How to Pass the Civil Service Exam

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject