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

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If we can make it by multiplying various other entirety numbers it is a Compowebsite Number.

Like this:

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Factors

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

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Prime Factorization


Example 1: What are the prime factors of 12 ?

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

12 ÷ 2 = 6

Yes, it divided precisely by 2. We have taken the first step!

But 6 is not a prime number, so we have to go better. Let"s try 2 again:

6 ÷ 2 = 3

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

12 = 2 × 2 × 3

As you have the right to check out, every factor is a prime number, so the answer must be right.

Note: 12 = 2 × 2 × 3 deserve to additionally 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 not. The answer need to be a whole number, and 73½ is not.

Let"s try the next prime number, 3:

147 ÷ 3 = 49

That operated, now we try factoring 49.

The following prime, 5, does not occupational. But 7 does, so we get:

49 ÷ 7 = 7

And that is as much as we need to go, because all the determinants are prime numbers.

147 = 3 × 7 × 7

(or 147 = 3 × 72 utilizing exponents)


Example 3: What is the prime factorization of 17 ?

Hang on ... 17 is a Prime Number.

So that is as much as we can go.

17 = 17


Anvarious other Method

We proved you just how to execute the factorization by founding at the smallest prime and also working upwards.

But periodically it is less complicated to break a number down right into any type of factors you deserve to ... then work-related those element down to primes.


Example: What are the prime determinants of 90 ?

Break 90 into 9 × 10

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

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


Factor Tree

And a "Factor Tree" can help: find any kind of factors of the number, then the components of those numbers, and so on, until we can not element any even more.


Example: 48

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

Now we continue and also element 8 right into 4 × 2

Then 4 into 2 × 2

And finally 6 right into 3 × 2

We can not element any kind of even more, so we have discovered 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 deserve to only be split by 1 or itself, so it cannot be factored any kind of further!

Every various other whole number have the right to be damaged dvery own right into prime number determinants.

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It is prefer the Prime Numbers are the fundamental structure blocks of all numbers.

This principle deserve to be extremely helpful once functioning via huge numbers, such as in Cryptography.

Cryptography

Cryptography is the examine of trick codes. Prime Factorization is incredibly necessary to human being who attempt to make (or break) trick codes based on numbers.

That is because factoring very big numbers is exceptionally tough, and also can take computer systems a long time to execute.

If you desire to understand even more, the topic is "encryption" or "cryptography".

Unique

And below is an additional thing:

Tbelow is just one (unique!) collection of prime factors for any kind of number.


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

330 = 2 × 3 × 5 × 11

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


In fact this principle is so vital it is called the Fundamental Theorem of Arithmetic.

See more: Which Of The Following Provides Evidence For Plate Tectonics ?

Prime Factorization Tool

OK, we have actually another approach ... usage our Prime Factorization Tool that have the right to work out the prime factors for numbers up to 4,294,967,296.


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