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

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If we can do it by multiply other whole numbers the is a Composite Number.

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## Factors

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

## Prime Factorization

### Example 1: What space the prime factors of 12 ?

It is best to start working from the the smallest prime number, i beg your pardon is 2, so let"s check:

12 ÷ 2 = 6

Yes, it divided exactly through 2. We have taken the very first step!

But 6 is no a element number, for this reason we must go further. Let"s shot 2 again:

6 ÷ 2 = 3

Yes, that operated also. And 3 is a prime number, so we have the answer:

12 = 2 × 2 × 3

As you have the right to see, every factor is a prime number, so the answer need to be right.

Note: 12 = 2 × 2 × 3 can likewise be written using exponents together 12 = 22 × 3

### Example 2: What is the element factorization the 147 ?

Can we division 147 precisely by 2?

147 ÷ 2 = 73½

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

Let"s try the following prime number, 3:

147 ÷ 3 = 49

That worked, now we shot factoring 49.

The next prime, 5, does not work. But 7 does, so we get:

49 ÷ 7 = 7

And that is as much as we should go, because all the components are element numbers.

147 = 3 × 7 × 7

(or 147 = 3 × 72 using exponents)

### Example 3: What is the prime factorization that 17 ?

Hang ~ above ... 17 is a prime Number.

So the is as far as we can go.

17 = 17

## Another Method

We confirmed you how to perform the administer by starting at the the smallest prime and working upwards.

But occasionally it is easier to break a number down into any factors you can ... Then work-related those element down to primes.

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

Break 90 right into 9 × 10

The prime components of 9 space 3 and also 3The prime factors of 10 are 2 and 5

So the prime components of 90 space 3, 3, 2 and 5

## Factor Tree

And a "Factor Tree" have the right to help: uncover any factors of the number, then the components of those numbers, etc, till we can"t factor any kind of more.

### Example: 48

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

Now we continue and factor 8 right into 4 × 2

Then 4 right into 2 × 2

And finally 6 into 3 × 2

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

Which reveals that 48 = 2 × 2 × 2 × 2 × 3

(or 48 = 24 × 3 making use of exponents)

## Why uncover Prime Factors?

A element number can only be divided by 1 or itself, so it cannot be factored any kind of further!

Every other totality number have the right to be broken down into prime number factors.

 It is prefer the element Numbers space the basic building blocks of all numbers.

This idea deserve to be really useful when working with huge numbers, such together in Cryptography.

## Cryptography

Cryptography is the study of mystery codes. Element Factorization is an extremely important to human being who try to make (or break) an enig codes based upon numbers.

That is due to the fact that factoring very big numbers is very hard, and also can take computers a long time to do.

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

## Unique

And here is one more thing:

There is only one (unique!) collection of prime determinants for any type of number.

Example The prime components of 330 room 2, 3, 5 and also 11:

330 = 2 × 3 × 5 × 11

There is no other possible set of element numbers that can be multiply to do 330.

In truth this idea is so necessary it is called the Fundamental to organize of Arithmetic.

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