Here's an algorithm in java:
import java.util.Scanner;
import java.util.ArrayList;
public class PrimeFactorization
{
public static void main(String[] args)
{
String response;
Scanner scan=new Scanner(System.in);
double num=0;
boolean read=false,run=true;
timer.start();
while(run)
{
System.out.println("Enter a number");
while(!read)
{
response=scan.next();
try
{
num=Double.parseDouble(response);
read=true;
}
catch(NumberFormatException exception)
{
System.out.println("Incorrect Format");
}
}
read=false;
TimerListener.resetT();
ArrayList<Double> list=getPrimeFactorization(num);
System.out.println("Prime Factorization:");
for(int count=0;count<list.size()-1;count++)
{
System.out.print(list.get(count)+", ");
}
System.out.println(list.get(list.size()-1));
System.out.println("Time: "+TimerListener.getT()+"s\n\n");
}
}
public static ArrayList<Double> getPrimeFactorization(double num)
{
ArrayList<Double> list=new ArrayList<Double>();
boolean run=true;
double index;
while (run)
{
list.add(index=getFirstFactor(num));
num=num/index;
if (num==1) run=false;
}
return list;
}
private static double getFirstFactor(double num)
{
for(int count=2;count<=Math.sqrt(num)+1;count++)
{
if ((double)num/(double)count%1==0)return count;
}
return num;
}
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
210 has sixteen factors.
Now that you know that 1, 2, 3, 5 and 7 are factors of 210, you need three more.
2 x 3 = 6
2 x 5 = 10
2 x 7 = 14
Divide all of those into 210 to get the other half.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
There's really only one way to find a prime factorization; divide prime numbers into a given number and its factors until all the factors are prime. There are numerous ways to notate that process. A quick glance through this website reveals continuous division, quotients of 1, Euclidean method, division ladders and the various factor trees, fireworks, rainbows, etc.
There are factor trees and ladders and rainbows and fireworks and they're all pretty much the same thing: ways to notate the process of finding the prime factorization of a given number. They differ in where they write the number and where the factors end up. In a factor tree, write the original number at the top and the bottommost branch will be the prime factorization. In a factor rainbow, write the original number at the bottom and the prime factorization will be the uppermost arc.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
The prime factorization of 4 is 2 x 2. It is not possible to find the LCM of a single number.
Find the prime factorization of 16.The prime factorization of 16 is: 2x2x2x2.
101 is already prime; no factorization required.
53 is a prime number so there is no relevant prime factorization for it.
prime factorization
find the prime factorization to the number 81
The prime factorization of 15332 • 17153 is not a prime number
The prime factorization of 6 is 2 x 3.
Only 23 has prime factorization of 23.
Since 5 is a prime number, the prime factorization of 5 is simply 5.
Prime factorization is when you find all the prime factors of a number.
The prime factorization of the number 33 is: 3 x 11
prime factorization each number is a part of the whole
29 is a prime number
None. 37 is a prime number.
2x3x5
The prime factorization of 4 is 2 x 2. It is not possible to find the LCM of a single number.