Basic Math 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