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Lecture Comments (8)

0 answers

Post by Bryan Burns on September 21, 2013

This is when I purchased "Mathematics for the Nonmathematician" ebook by Morris Kline to get a full picture of mathematics, it's history and practice use. This in reaction to al gut's question on concept building and a desire to understand the entire picture.

1 answer

Last reply by: Leif Djurhuus
Wed Aug 21, 2013 4:08 AM

Post by Herson Ricardo Alarcon on March 19, 2013

in example one could u put 2x5x5 or those the highest # goes first

0 answers

Post by carreola arreola on July 24, 2012

best teacher ever

0 answers

Post by ozgur kuzu on June 5, 2012

great teaching )

2 answers

Last reply by: Sohaib Muhammad Pervaiz
Mon Oct 14, 2013 11:32 AM

Post by al gut on December 4, 2010

You need more concept building. What is the purpose of prime factorization? What is the end game?

Prime Factorization

Related Links

  • Prime number: A number that has no factors besides 1 and itself
  • Composite number: A number that has more factors besides 1 and itself
  • Factor: A part of a number that can be divided out without leaving a remainder
  • Product: The resulting number when you multiply two numbers together
  • Factor tree: A factoring method used to find the product of prime numbers

Prime Factorization

Find the prime factorization of 60
  • 6 ×10
6 × 5 × 2
Find the prime factorization of 45
  • 5 ×9
  • 5 ×3 ×3
5 ×32
Find the prime factorization of 42
  • 7 ×6
7 × 3 × 2
Find the prime factorization of 18
  • 3 ×6
  • 3 ×3 ×2
32 ×2
Find the prime factorization of 14
2 × 7
Find the prime factorization of 45
  • 5 ×9
  • 5 ×3 ×3
5 ×32
Find the prime factorization of 24
  • 3 ×8
  • 3 ×4 ×2
  • 3 ×2 ×2 ×2
3 ×23
Find the prime factorization of 56
  • 7 ×8
  • 7 ×4 ×2
  • 7 ×2 ×2 ×2
7 ×23
Find the prime factorization of 81
  • 9 ×9
  • 3 ×3 ×9
  • 3 ×3 ×3 ×3
34
Find the prime factorization of 16
  • 4 ×4
  • 2 ×2 ×4
  • 2 ×2 ×2 ×2
24

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Prime Factorization

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Terms to Review 0:07
    • Prime vs. Composite
    • Factor
    • Product
  • Factor Tree 1:39
    • Example: Prime Factorization
    • Example: Prime Factorization
  • Extra Example 1: Prime Factorization 4:08
  • Extra Example 2: Prime Factorization 5:05
  • Extra Example 3: Prime Factorization 5:33
  • Extra Example 4: Prime Factorization 6:13

Transcription: Prime Factorization

Welcome back; this is a lesson on prime factorization.0000

Before we begin, let's go over some terms: prime and composite.0008

Prime number we know is a number that has no factors besides 1 and itself.0014

For example, the number 5.0022

5 only has the factors 1 and itself so that is considered a prime number.0025

A composite number is a number that has more factors than 1 and itself.0031

For example, the number 10.0036

10 is a composite number because we know that the number 2 is a factor of 10 and 5 is a factor of 10.0039

So 10 would be considered a composite number.0051

A factor then would be all the number parts that go into a given number.0054

If we have again 10, the factors would be 1, 2, 5, and 10.0062

These are all considered factors of the number 10.0071

Product; product is a number where we multiply numbers together.0076

The product of 2 and 5 is 10.0084

So product, you just multiply the numbers together.0092

The method in solving prime factorization is called the factor tree.0100

The factor tree... we all know what a tree looks like.0106

It is going to branch out into a bunch of factors.0109

More specifically, prime factors, which is why it is called prime factorization.0115

Let's start off with the number 10.0121

I want to break this up into factor pairs; say 5 and 2.0125

Once I have a prime number, I want you to circle it.0133

We know 5 is a prime number; we know 2 is a prime number.0137

Once all the numbers are circled, we know that we have only prime numbers.0142

Then we are done; all we have to do is write out the answer.0148

10, the prime factorization of 10 would be 5 times 2.0155

Another example, 24; 24 has a few different factor pairs.0164

You can choose whichever one; let's go with 6 and 4.0172

6 and 4, we know that both are not prime numbers.0178

They are composite numbers; we have to break them up even further.0182

I am going to branch it out again.0186

6 is going to break up into 3 and 2.0189

This is a prime number; I am going to circle it.0194

This is a prime number.0196

Then 4, I am going to break up into 2 and 2.0199

A prime number, I circle this and that.0205

All I have left are prime numbers.0211

The prime factorization of 24 would be 3 times 2 times 2 times 2.0215

Since I have the same numbers here, I can write this in scientific notation.0225

This can be also 3 times 2 to the 3rd power because I have three 2s.0232

Here is an example.0248

If you can, I want you to pause the video and I want you to try this problem on your own.0252

Let's go over this now; 50.0259

I am going to break this up into a factor pair; let's say 5 and 10.0264

5 is a prime number; circle that one.0271

10, I am going to break this up even further to 2 and 5.0275

I end up circling those.0283

50 becomes 5 times 5 times 2 or I can write it as 52 times 2.0286

Here is another example; 15.0307

15, I can only break it up into 5 and 3.0313

They are both prime numbers; this was an easy one.0320

15 becomes 5 and 3; let's do a couple more examples.0324

The number 12 becomes 4 and 3; you can also do 6 and 2.0337

You are still going to get the same answer.0350

3 is a prime number; I am going to circle that one.0353

4 becomes 2 and 2; circle those; I have nothing else left.0356

The prime factorization of 12 is 22 times 3.0363

One more example, 36.0373

36, again you have a couple different options; let's go with 6 and 6.0378

6, I can break up into 3 and 2; I am going to circle those.0387

This 6 also to 3 and 2.0395

36 becomes 3 times 3 times 2 times 2.0401

This is the same thing as 32 times 22.0412

That is it for prime factorization.0418