The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 và 23, & we have a prime number chart if you need more.Bạn đã xem: Prime numbers là gì

If we **can** make it by multiplying other whole numbers it is a **Composite Number**.

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## Prime Factorization

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

It is best lớn start working from the smallest prime number, which is 2, so let"s check:

12 ÷ 2 = 6

Yes, it divided exactly 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. & 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 exactly by 2?

147 ÷ 2 = 73½

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

Let"s try the next prime number, 3:

147 ÷ 3 = 49

That worked, now we try factoring 49.

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

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 Method

**But sometimes it is easier to lớn break a number down into any factors** you can ... Then work those factor down to lớn primes.

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

Break 90 into 9 × 10

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

So the prime factors of 90 are **3, 3, 2 và 5**

## Factor Tree

**And 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" & "6" below 48

Now we continue & 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**

(or **48 = 24 × 3** using exponents)

## 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 lượt thích the Prime Numbers are the basic building blocks of all numbers. |

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

## Cryptography

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

That is because factoring very large numbers is very hard, và can take computers a long time khổng lồ do.

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

## Unique

And here is another thing:

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

Example The prime factors of 330 are 2, 3, 5 và 11:

330 = 2 × 3 × 5 × 11

There is no other possible set of prime numbers that can be multiplied to make 330.

**In fact this idea is so important it is called the Fundamental Theorem of Arithmetic**.

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## Prime Factorization Tool

OK, we have one more method ... Use our Prime Factorization Tool that can work out the prime factors for numbers up to 4,294,967,296.

Prime và Composite Numbers Prime Numbers Chart Prime Factorization Tool Divisibility Rules