logo
g Text Version
Beauty & Self
Books & Music
Career
Computers
Education
Family
Food & Wine
Health & Fitness
Hobbies & Crafts
Home & Garden
Money
News & Politics
Relationships
Religion & Spirituality
Sports
Travel & Culture
TV & Movies

dailyclick
Bored? Games!
Nutrition
Postcards
Take a Quiz
Rate My Photo

new
European Travel
Action Movies
Bible Basics
Houseplants
Romance Movies
Creativity
Family Travel


dailyclick
All times in EST

Full Schedule
g
g Math Site

BellaOnline's Math Editor

g

Prime Factorization


Prime Factorization is used to find the Least Common Multiple and the Greatest Common Factor. This lesson will address a few definitions, give how-to instructions, detailed examples, and share a website for online practice.

Prime Numbers
Prime numbers have only two factors. Those factors are one and itself. For example, 17 has the factors 1 and 17 only. Thus, 17 is a prime number. Likewise, 2, 3, 5, 7, 11, 13, 17, 19 are prime numbers too. The number 39 has factors 1, 3, 13, and 39. Thus, 39 is not a prime number.

Composite numbers
Numbers with other factors besides themselves and one are called composite numbers.
Therefore, 39 is a composite number. By the way, one is not a prime or composite number.

Prime Factorization ---------------------Usefulness: to find the Greatest Common Factor or Least Common Multiple

When a composite number is factored using only prime numbers such as 2 x 3 x 5 = 30, it is referred to as prime factorization.

How to Find the Prime Factorization of a Number

1) Start with the smallest prime number, 2, and ask yourself if the prime number can divide into the given number without a remainder. In other words, is it divisible by 2?

2) If no, then the prime number is not a factor. Try the next prime number.

3) If yes, then include that prime number in the prime factorization equation.

4) If the given number was divisible by the prime number in step one, was the answer a composite or prime number? If composite, use this number and repeat steps 1 – 3 starting with the prime number 2 again.

If the answer is a prime number, divide the number by itself to get one and you are finished; include all prime numbers in the factorization.

5) Check – compute the multiplication sentence and the answer should equal the number just factored.

Let’s find the prime factorization of 30

1) Start with the smallest prime number 2. Ask yourself if the prime number can divide into 30 without a remainder. 30 / 2 = 15 remainder 0

3) Yes it can. Then include 2 in the prime factorization equation.

4) In step 1,was the answer a composite or prime number? 15 is a composite number. So, repeat the process with 15 starting with 2 again.

15 / 2 = 7 remainder 1; 15 is not divisible by 2; so, 2 won’t be used again

Next, try 3; 15 / 3 = 5; 15 is divisible by 3; 3 becomes part of the factorization.

The answer 5 is prime; so, divide 5 by itself ----- 5 / 5 =1

You are finished; include all prime numbers in the factorization.
Summary:
30/ 2 = 15
15/ 3 = 5
5 / 5 = 1
The prime factorization of 30 = 2 x 3 x 5.

The bold numbers are the prime factors of 30.
Check – compute the multiplication sentence and the answer should equal the number just factored, 30.


Example 2: Find the prime factorization of 45

45 / 3 = 15
15 / 3 = 5
5 / 5 = 1
Prime factorization of 45 = 3 x 3 x 5


Example 3: Find the prime factorization of 88

82 / 2 = 44
44 / 2 = 22
22 / 2 = 11
11/ 11 = 1
Prime factorization of 88 = 2 x 2 x 2 x 11.

For online practice: I highly recommend the website in the related links section. It uses the factor tree method which is similar to the above method.
Add Prime+Factorization to Twitter Add Prime+Factorization to Facebook Add Prime+Factorization to MySpace Add Prime+Factorization to Del.icio.us Digg Prime+Factorization Add Prime+Factorization to Yahoo My Web Add Prime+Factorization to Google Bookmarks Add Prime+Factorization to Stumbleupon Add Prime+Factorization to Reddit




Practice - Prime Factorization
Fractions - Adding Unlike Denominators
Fractions - Subtracting Mixed Numbers
RSS
Related Articles
Editor's Picks Articles
Top Ten Articles
Previous Features
Site Map


For FREE email updates, subscribe to the Math Newsletter


Past Issues


print
Printer Friendly
bookmark
Bookmark
tell friend
Tell a Friend
forum
Forum
email
Email Editor


Content copyright © 2014 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.

g


g features
Intro to Algebra Crossword Puzzle- 1

Math MOOC - Free Online Math Courses - Self-Paced

Interactive App for Student Engagement

Archives | Site Map

forum
Forum
email
Contact

Past Issues
memberscenter


vote
Poetry
Daily
Weekly
Monthly
Less than Monthly



BellaOnline on Facebook
g


| About BellaOnline | Privacy Policy | Advertising | Become an Editor |
Website copyright © 2014 Minerva WebWorks LLC. All rights reserved.


BellaOnline Editor