Skip to main content

Prime Factorization

Prime Numbers

A Prime Number can be divided evenly only by 1 or itself.
And it must be a whole number greater than 1.
The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ..., and we have a prime number chart if you need more.

Factors

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

Prime Factorization

"Prime Factorization" is finding which prime numbers multiply together to make the original number.
Here are some examples:

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 evenly 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. 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 evenly by 2? No, so we should try the next prime number, 3:
147 ÷ 3 = 49
Then we try factoring 49, and find that 7 is the smallest prime number that works:
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

We showed you how to do the factorization by starting at the smallest prime and working upwards.
But sometimes it is easier to break a number down into any factors you can ... then work those factor down to primes.

Example: What are the prime factors of 90 ?

Break 90 into 9 × 10
  • The prime factors of 9 are 3 and 3
  • The prime factors of 10 are 2 and 5
So the prime factors of 90 are 3, 3, 2 and 5

Comments

Post a Comment

Popular posts from this blog

Computer Buses

Computer Buses   A computer system consists of different devices.CPU must be able to communicate with all devices. The devices are connected together by a communications channel called bus. A bus consists of a set of communication lines or wires. It is used to move a large amount of bits in the form of electrical pulses from one unit to another. The bus is used to connect the following units: Central Processing Unit Control Unit  Arithmetic and Logic Unit Main Memory ( RAM, ROM) Input / Output Devices Bus is a common path to transfer data and commands between CPU, memory and input / output devices.It is also used to send or receive data from secondary storage.The capacity of a bus depends on the number of data lines in it.A bus with 16 lines can carry 16 bits or 2 bytes at a time. A bus with 32 lines can carry 32 bits or 4 bytes at a time . Types Of  Buses Different types of buses are as follows: 1. Data Bus 2.Addres...
Post a Comment
Read more

Steps of splitting pdf files

Goto https://www.ilovepdf.com/split_pdf Click on Select PDF File. Upload your pdf file here. Select Extract Pages from right menu. Click on Split pdf button and wait for the procedure. Now Click on Download Split PDF and you will get a zip file in which there will be separate pdf.
Post a Comment
Read more

Steps to remove google accounts from Computer

Open Google . You will see a round shaped picture of google account picture in top right corner as marked in below picture Click on it. Click on sign out of all accounts Click on Sign In at the top right corner as shown in picture below. Click on it. You will see following screen. Select your desired account from it and sign in . Reopen your form by clicking link provided to you, It will be open now.
Post a Comment
Read more