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Prime number là gì

15:55, 23/10/2021

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 and 23, and we have sầu a prime number chart if you need more.quý khách vẫn xem: Prime Number In Vietnamese

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 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 sầu 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 sầu 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, and 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 khổng lồ break a number down inkhổng lồ any factors you can ... then work those factor down to primes.

Example: What are the prime factors of 90 ?

Break 90 into lớn 9 × 10

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

So the prime factors of 90 are 3, 3, 2 and 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


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48 = 8 × 6, so we write down "8" and "6" below 48

Now we continue & factor 8 inkhổng lồ 4 × 2

Then 4 inkhổng lồ 2 × 2

And lastly 6 inlớn 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.


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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 to people who try khổng lồ 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 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 và 11:

330 = 2 × 3 × 5 × 11

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

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

Prime Factorization Tool

OK, we have sầu 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 và Composite Numbers Prime Numbers Chart Prime Factorization Tool Divisibility Rules