# Online Pre-Algebra Tutoring: Factoring the Prime

Home | Online Math Tutoring | Pre-Algebra Tutoring | **Prime Factorization**

## Learn about Factoring the Prime from Certified Online Pre-Algebra Tutor

Prime factorization of a whole number means to write it as the product of only prime numbers. A composite number can be written as a product of all of its prime factors.

To find the **prime factorization** of a number:

Divide the number by prime factors until the quotient is 1.

#### Let’s understand with an example

#### What is the prime factorization of 45?

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

The prime factorization of 45 is:

**45 = 3 × 3× 5**

This can also be written using exponents as:

**45 = 3 ^{2} × 5**

**Factor Trees**

**Another method for producing the prime factorization of a natural number is to use what is called a factor tree.**

A factor tree is a tool that breaks down any number into its prime factors

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring. These two factors are the first branching in the factor tree. There are often several different pairs of factors that we could choose to begin the process. The choice does not matter; we may begin with any two factors. We repeat the process with each factor until each branch of the tree ends in a prime. Then the prime factorization is complete.

#### Example: Prime factorization of 24

The prime factorization is the product of the circled primes

**So the prime factorization of 24 is 24 = 2 ×2 ×2 × 3 = 2 ^{3} × 3.**

#### Check Point

- What is the prime factorization of 86?
- What is the prime factorization of 592?
- What is the prime factorization of 225?
- What is the prime factorization of 1050?
- What is the prime factorization of 42 use the factor tree method

## Why learn with eTutorWorld ?

- Meet your online expert tutor from the comfort and safety of your home
- Schedule sessions at your convenient date and time
- Access recordings of sessions for a month from session date
- Receive a personalized practice sheet after every tutoring session
- Call/chat us on our 24 X 7 support (+1.269.763.4602) to resolve issues or ask questions
- Experience the state-of-the-art technology by learning over LIVE tutoring sessions
- Get a 30 day Money Back Guarantee on our online tutoring services

*No credit card, nor any obligation to purchase. *

*Schedule your FREE TRIAL session to meet an expert LIVE tutor & get all the help you want. *

Our Learning by Design methodology focuses exclusively on individual students.

Our expert tutors are specially trained to identify and diagnose the needs and skills of each student and plan future tutoring lessons accordingly.

Know more about our Personalised Online Tutoring Packs.

+1-269-763-4602

+1-269-763-5024

#### Quick Links

#### Follow Us

© 2020 eTutorWorld - Online Tutoring and Test Prep | All rights reserved