# PRIME NUMBER LÀ GÌ

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 và 23, và we have sầu a prime number chart if you need more.quý khách hàng 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 to 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 khổng lồ 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 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 lớn 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 lớn break a number down inlớn any factors** you can ... then work those factor down to primes.

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

Break 90 inlớn 9 × 10

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

So the prime factors of 90 are **3, 3, 2 & 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 and factor 8 into lớn **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.

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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 like 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 lớn people who try lớn make (or break) secret codes based on numbers.

That is because factoring very large numbers is very hard, & can take computers a long time to lớn vì chưng.

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

## Unique

And here is another thing:

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

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

330 = 2 × 3 × 5 × 11

There is no other possible mix of prime numbers that can be multiplied lớn 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 lớn 4,294,967,296.

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