The Fundamental Theorem of Arithmetic states that any positive integer can be expressed as the product of prime numbers. This program will use a while loop structure to produce the prime factorization of a positive integer provided by the user. You may remember having done this using “Factor Trees"

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PRIME FACTORIZATION PROGRAM
The Fundamental Theorem of Arithmetic states that any positive integer can be
expressed as the product of prime numbers. This program will use a while loop
structure to produce the prime factorization of a positive integer provided by the
user. You may remember having done this using "Factor Trees"
The Algorithm:
1. Obtain a positive integer from the user.
2. For every number from 2 up to the positive integer:
A. Determine if the number is a factor (HOW?). If it is:
1. List the number as a factor.
2. Divide the number out of the positive integer.
3. Determine if the integer is a prime number (only factor being itself and 1).
Examples:
For the positive integer 30
30 % 2 = 0 Therefore 2 is a factor
30 /2 = 15
15 % 3 = 0 Therefore 3 is a factor
15/3 = 5
This means we're
5 % 5 = 0
Therefore 5 is a factor
5/5 = 1 + done!!!
Transcribed Image Text:PRIME FACTORIZATION PROGRAM The Fundamental Theorem of Arithmetic states that any positive integer can be expressed as the product of prime numbers. This program will use a while loop structure to produce the prime factorization of a positive integer provided by the user. You may remember having done this using "Factor Trees" The Algorithm: 1. Obtain a positive integer from the user. 2. For every number from 2 up to the positive integer: A. Determine if the number is a factor (HOW?). If it is: 1. List the number as a factor. 2. Divide the number out of the positive integer. 3. Determine if the integer is a prime number (only factor being itself and 1). Examples: For the positive integer 30 30 % 2 = 0 Therefore 2 is a factor 30 /2 = 15 15 % 3 = 0 Therefore 3 is a factor 15/3 = 5 This means we're 5 % 5 = 0 Therefore 5 is a factor 5/5 = 1 + done!!!
Some things to think about:
What should my condition be in my while loop?
What do I do if a prime factor occurs more than once?
( 24 = 2 x 2 x 2 x 3 )
How can I make the program as efficient as possible?
Be sure to use good JAVA style and include plenty of comments!!
The output should be similar to the example below:
Enter a positive integer: 150
150 = 2 x 3 x 5 x 5
150 is not a prime number.
Write your algorithm in pseudocode below. Clearly indicate any loop
structures or conditional statements.
Transcribed Image Text:Some things to think about: What should my condition be in my while loop? What do I do if a prime factor occurs more than once? ( 24 = 2 x 2 x 2 x 3 ) How can I make the program as efficient as possible? Be sure to use good JAVA style and include plenty of comments!! The output should be similar to the example below: Enter a positive integer: 150 150 = 2 x 3 x 5 x 5 150 is not a prime number. Write your algorithm in pseudocode below. Clearly indicate any loop structures or conditional statements.
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