## Prime Factorization

"Prime Factorization" is finding

Here are some examples:

Example 1: What are the prime factors of 12 ? It is best to start working from the smallest prime number, which is 2, so let's check:

12 ÷ 2 = 6

Yes, it divided evenly by 2. We have taken the first step!

But 6 is not a prime number, so we need to go further. Let's try 2 again:

6 ÷ 2 = 3

Yes, that worked also. And 3

As you can see,

Note:

Example 2: What is the prime factorization of 147 ? Can we divide 147 evenly by 2? No, so we should try the next prime number, 3:

147 ÷ 3 = 49

Then we try factoring 49, and find that 7 is the smallest prime number that works:

49 ÷ 7 = 7

And that is as far as we need to go, because all the factors are prime numbers.

(or

Example 3: What is the prime factorization of 17 ? Hang on ...

So that is as far as we can go.

**which prime numbers**multiply together to make the original number.Here are some examples:

Example 1: What are the prime factors of 12 ? It is best to start working from the smallest prime number, which is 2, so let's check:

12 ÷ 2 = 6

Yes, it divided evenly by 2. We have taken the first step!

But 6 is not a prime number, so we need to go further. Let's try 2 again:

6 ÷ 2 = 3

Yes, that worked also. And 3

**is**a prime number, so we have the answer:**12 = 2 × 2 × 3**As you can see,

**every factor**is a**prime number**, so the answer must be right.Note:

**12 = 2 × 2 × 3**can also be written using exponents as**12 = 22 × 3**Example 2: What is the prime factorization of 147 ? Can we divide 147 evenly by 2? No, so we should try the next prime number, 3:

147 ÷ 3 = 49

Then we try factoring 49, and find that 7 is the smallest prime number that works:

49 ÷ 7 = 7

And that is as far as we need to go, because all the factors are prime numbers.

**147 = 3 × 7 × 7**(or

**147 = 3 × 72**using exponents)Example 3: What is the prime factorization of 17 ? Hang on ...

**17 is a Prime Number**.So that is as far as we can go.

**17 = 17**