The first couple of prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 and 23, and we have actually a prime number chart if you require more.

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If us **can** make it by multiply other entirety numbers it is a **Composite Number**.

Like this:

## Factors

"Factors" space the numbers you multiply together to get an additional number:

## Prime Factorization

### Example: What room the prime components of 12 ?

It is best to begin working from the the smallest prime number, i m sorry is 2, for this reason let"s check:

12 ÷ 2 = 6

Yes, it split exactly by 2. We have taken the first step!

But 6 is no a element number, therefore we must go further. Let"s try 2 again:

6 ÷ 2 = 3

Yes, that functioned also. And 3 **is** a element number, for this reason we have the answer:

**12 = 2 × 2 × 3**

As you deserve to see, **every factor** is a **prime number**, so the answer must be right.

Note: **12 = 2 × 2 × 3** can additionally be written using exponents as **12 = 22 × 3**

### Example: What is the prime factorization that 147 ?

Can we division 147 precisely by 2?

147 ÷ 2 = 73½

No that can"t. The answer should be a whole number, and 73½ is not.

Let"s try the next prime number, 3:

147 ÷ 3 = 49

That worked, now we shot factoring 49.

The following prime, 5, does not work. But 7 does, so us get:

49 ÷ 7 = 7

And that is as much as we must go, because all the factors are prime numbers.

**147 = 3 × 7 × 7**

(or **147 = 3 × 72** utilizing exponents)

### Example: What is the element factorization that 17 ?

Hang on ... **17 is a element Number**.

So that is as far as we can go.

**17 = 17**

## Another Method

We proved you how to do the factorization by starting at the smallest prime and also working upwards.

But periodically it is easier to break a number down into **any factors** you have the right to ... Then work those aspect down to primes.

### Example: What are the prime factors of 90 ?

Break 90 right into 9 × 10

The prime determinants of 9 are**3 and 3**The prime factors of 10 space

**2 and 5**

So the prime components of 90 room **3, 3, 2 and 5**

## Factor Tree

And a "Factor Tree" deserve to help: find **any factors** of the number, climate the factors of those numbers, etc, till we can"t factor any more.

### Example: 48

**48 = 8 × 6**, so we compose down "8" and also "6" listed below 48

Now us continue and also factor 8 into **4 × 2**

Then 4 into **2 × 2**

And ultimately 6 right into **3 × 2**

We can"t factor any type of more, so us have uncovered the prime factors.

Which reveals the **48 = 2 × 2 × 2 × 2 × 3**

(or **48 = 24 × 3** utilizing exponents)

## Why find Prime Factors?

A element number deserve to only be split by 1 or itself, so it can not be factored any kind of further!

Every other entirety number can be broken down right into prime number factors.

It is prefer the prime Numbers are the |

This idea have the right to be very useful when working with large numbers, such as in Cryptography.

## Cryptography

Cryptography is the examine of mystery codes. Prime Factorization is very important to people who try to make (or break) an enig codes based on numbers.

That is since factoring very huge numbers is very hard, and also can take computer systems a long time to do.

If you desire to understand more, the subject is "encryption" or "cryptography".

## Unique

And right here is another thing:

**There is just one (unique!) set of prime components for any kind of number.**

### Example: the prime factors of 330 are 2, 3, 5 and 11

330 = 2 × 3 × 5 × 11

There is no other possible set of element numbers that have the right to be multiplied to do 330.

In reality this idea is so vital it is called the **Fundamental organize of Arithmetic**.

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## Prime factorization Tool

OK, we have actually one more method ... Use our prime Factorization tool that have the right to work the end the prime factors for numbers up to 4,294,967,296.

370, 1055, 1694, 1695, 1696, 1697

Prime and also Composite Numbers element Numbers Chart element Factorization tool Divisibility Rules