Prime FactorizationPrime NumbersA Prime Number can be divided evenly

And it must be a whole number greater than 1.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ..., and we have a prime number chart if you need more.

Factors"Factors" are the numbers you multiply together to get another number:

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.

Another MethodWe showed you how to do the factorization by starting at the smallest prime and working upwards.

But sometimes it is easier to break a number down into

Example: What are the prime factors of 90 ?Break 90 into 9 × 10

Factor TreeAnd a "Factor Tree" can help: find

Example: 48

Now we continue and factor 8 into

Then 4 into

And lastly 6 into

We can't factor any more, so we have found the prime factors.

Which reveals that

Why find Prime Factors?A prime number can only be divided by 1 or itself, so it cannot be factored any further!

Every other whole number can be broken down into prime number factors.

It is like the Prime Numbers are the

This can be very useful when working with big numbers, such as in Cryptography.

CryptographyCryptography is the study of secret codes. Prime Factorization is very important to people who try to make (or break) secret codes based on numbers.

That is because factoring very large numbers is very hard, and can take computers a long time to do.

If you want to know more, the subject is "encryption" or "cryptography".

UniqueAnd here is another thing:

**only**by 1 or itself.And it must be a whole number greater than 1.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ..., and we have a prime number chart if you need more.

Factors"Factors" are the numbers you multiply together to get another number:

Prime Factorization"Prime Factorization" is finding

**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**Another MethodWe showed you how to do the factorization by starting at the smallest prime and working upwards.

But sometimes it is easier to break a number down into

**any factors**you can ... then work those factor down to primes.Example: What are the prime factors of 90 ?Break 90 into 9 × 10

- The prime factors of 9 are
**3 and 3** - The prime factors of 10 are
**2 and 5**

**3, 3, 2 and 5**Factor TreeAnd a "Factor Tree" can help: find

**any factors**of the number, then the factors of those numbers, etc, until we can't factor any more.Example: 48

**48 = 8 × 6**, so we write down "8" and "6" below 48Now we continue and factor 8 into

**4 × 2**Then 4 into

**2 × 2**And lastly 6 into

**3 × 2**We can't factor any more, so we have found the prime factors.

Which reveals that

**48 = 2 × 2 × 2 × 2 × 3**Why find Prime Factors?A prime number can only be divided by 1 or itself, so it cannot be factored any further!

Every other whole number can be broken down into prime number factors.

It is like the Prime Numbers are the

**basic building blocks**of all numbers.This can be very useful when working with big numbers, such as in Cryptography.

CryptographyCryptography is the study of secret codes. Prime Factorization is very important to people who try to make (or break) secret codes based on numbers.

That is because factoring very large numbers is very hard, and can take computers a long time to do.

If you want to know more, the subject is "encryption" or "cryptography".

UniqueAnd here is another thing:

**There is only one (unique!) set of prime factors for any number.**