PRIME FACTOR LÀ GÌ

     

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 và 23, and we have a prime number chart if you need more.

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

Like this:


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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 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, 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 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.

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17 = 17

Another Method

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

Example: What are the prime factors of 90 ?

Break 90 into 9 × 10

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


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


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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 lớn 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 to do.

If you want lớn 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 mix of prime numbers that can be multiplied lớn make 330.

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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