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Q: What is primefactorization?

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18

3.5.5

dx suck it

2, 2, 19

5 x 13 = 65

28 = 256

The prime factorization of 95 is 1,5,19.

factoring 85 85=5*17

It is: 2*2*5*5*7 = 700

5 and 25

5 x 5 x 7 = 175

5 times 5 times 2 times 2

As a product of its prime factors: 3*3*101 = 909

As a product of its prime factors: 5*5*5*11*13 = 17875

2 x 2 x 2 x 3 x 5 = 120

The prime factorization of 378 using exponents is 21 x 33 x 71

since 144 is 122 you can find the primefactorization easy by noting that 12=22 x3 so 144=24x32

88 2 x 44 2 x 4 x 11 2 x 2 x 2 x 11

A very fast and effective way to do this would be a factor tree. I can't draw it on here, as I have no tools, but here is a crude example: 114= 6 * 19 2 * 3 * 19 Here is an explanation in words: 114/6=19, hence 114= 6 * 19 If you have ever been taught how to prime factorize, you must know to reduce it to prime numbers. 19 is already a prime number, so you leave it alone. 6 is not, and the primefactorization of 6 is 2*3, hence the prime factorization of 114 is 2*3*19. It is simple if you know how to prime factorize.

Factorization of 512Factorization of 512 is:1 X 5122 X 2564 X 1288 X 6416 X 32Factorization is not to be confused with primefactorization. Prime factorization for 512 is:2 X 2562 X 2 X 1282 X 2 X 2 X 642 X 2 X 2 X 2 X 322 X 2 X 2 X 2 X 2 X 162 X 2 X 2 X 2 X 2 X 2 X 82 X 2 X 2 X 2 X 2 X 2 X 2 X 42 X 2 X 2 x 2 X 2 X 2 X 2 X 2 X 2 or 29

Knowing When Factorization is PrimeFactorization is prime factorization when all the factors are prime numbers. If there is just one composite number in the factorization, it is not prime.A couple of examples:12 - 2 X 6 = 12. 2 is prime, but 6 is composite, so more factoring is needed.2 X 2 X 3 = 12. Numbers 2 and 3 are prime, so prime factorization is complete.Always starting with the lowest factor of the number (except for 1) makes this easy.For example, the number 100. You can start with any of its factors, but the lowest one is 2, so start with it.100 - 2 X 50 = 100. 50 is a composite number, so it must be factored. 2 is the lowest factor (besides 1), so use it.2 X 2 X 25 = 100. Now, 25 needs to be factored, but the lowest factor is not 2, but 5, so use it.2 X 2 X 5 X 5 All numbers are now prime, so the prime factorization of 100 is:2 X 2 X 5 X 5. You can also write it with exponents like this: 22 X 52

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; }

Basic factoring will be automatically and instantaneously completed through this applet: http://conceptualeclipse.googlepages.com/primefactorization (no download necessary, works on all platforms) The applet will clearly tell you the prime factors, number of prime factors, and number of unique prime factors of any integer between -1,000,000,000 and 1,000,000,000 immediately. For convenience's sake, here is a list of the factors of all numbers between 1 and 100 They are presented in the following format Number X ---First factor of number X ---Second factor of number X ---Third factor of number X 1 ---1 2 ---1 ---2 3 ---1 ---3 4 ---1 ---2 ---4 5 ---1 ---5 6 ---1 ---2 ---3 ---6 7 ---1 ---7 8 ---1 ---2 ---4 ---8 9 ---1 ---3 ---9 10 ---1 ---2 ---5 ---10 11 ---1 ---11 12 ---1 ---2 ---3 ---4 ---6 ---12 13 ---1 ---13 14 ---1 ---2 ---7 ---14 15 ---1 ---3 ---5 ---15 16 ---1 ---2 ---4 ---8 ---16 17 ---1 ---17 18 ---1 ---2 ---3 ---6 ---9 ---18 19 ---1 ---19 20 ---1 ---2 ---4 ---5 ---10 ---20 21 ---1 ---3 ---7 ---21 22 ---1 ---2 ---11 ---22 23 ---1 ---23 24 ---1 ---2 ---3 ---4 ---6 ---8 ---12 ---24 25 ---1 ---5 ---25 26 ---1 ---2 ---13 ---26 27 ---1 ---3 ---9 ---27 28 ---1 ---2 ---4 ---7 ---14 ---28 29 ---1 ---29 30 ---1 ---2 ---3 ---5 ---6 ---10 ---15 ---30 31 ---1 ---31 32 ---1 ---2 ---4 ---8 ---16 ---32 33 ---1 ---3 ---11 ---33 34 ---1 ---2 ---17 ---34 35 ---1 ---5 ---7 ---35 36 ---1 ---2 ---3 ---4 ---6 ---9 ---12 ---18 ---36 37 ---1 ---37 38 ---1 ---2 ---19 ---38 39 ---1 ---3 ---13 ---39 40 ---1 ---2 ---4 ---5 ---8 ---10 ---20 ---40 41 ---1 ---41 42 ---1 ---2 ---3 ---6 ---7 ---14 ---21 ---42 43 ---1 ---43 44 ---1 ---2 ---4 ---11 ---22 ---44 45 ---1 ---3 ---5 ---9 ---15 ---45 46 ---1 ---2 ---23 ---46 47 ---1 ---47 48 ---1 ---2 ---3 ---4 ---6 ---8 ---12 ---16 ---24 ---48 49 ---1 ---7 ---49 50 ---1 ---2 ---5 ---10 ---25 ---50 51 ---1 ---3 ---17 ---51 52 ---1 ---2 ---4 ---13 ---26 ---52 53 ---1 ---53 54 ---1 ---2 ---3 ---6 ---9 ---18 ---27 ---54 55 ---1 ---5 ---11 ---55 56 ---1 ---2 ---4 ---7 ---8 ---14 ---28 ---56 57 ---1 ---3 ---19 ---57 58 ---1 ---2 ---29 ---58 59 ---1 ---59 60 ---1 ---2 ---3 ---4 ---5 ---6 ---10 ---12 ---15 ---20 ---30 ---60 61 ---1 ---61 62 ---1 ---2 ---31 ---62 63 ---1 ---3 ---7 ---9 ---21 ---63 64 ---1 ---2 ---4 ---8 ---16 ---32 ---64 65 ---1 ---5 ---13 ---65 66 ---1 ---2 ---3 ---6 ---11 ---22 ---33 ---66 67 ---1 ---67 68 ---1 ---2 ---4 ---17 ---34 ---68 69 ---1 ---3 ---23 ---69 70 ---1 ---2 ---5 ---7 ---10 ---14 ---35 ---70 71 ---1 ---71 72 ---1 ---2 ---3 ---4 ---6 ---8 ---9 ---12 ---18 ---24 ---36 ---72 73 ---1 ---73 74 ---1 ---2 ---37 ---74 75 ---1 ---3 ---5 ---15 ---25 ---75 76 ---1 ---2 ---4 ---19 ---38 ---76 77 ---1 ---7 ---11 ---77 78 ---1 ---2 ---3 ---6 ---13 ---26 ---39 ---78 79 ---1 ---79 80 ---1 ---2 ---4 ---5 ---8 ---10 ---16 ---20 ---40 ---80 81 ---1 ---3 ---9 ---27 ---81 82 ---1 ---2 ---41 ---82 83 ---1 ---83 84 ---1 ---2 ---3 ---4 ---6 ---7 ---12 ---14 ---21 ---28 ---42 ---84 85 ---1 ---5 ---17 ---85 86 ---1 ---2 ---43 ---86 87 ---1 ---3 ---29 ---87 88 ---1 ---2 ---4 ---8 ---11 ---22 ---44 ---88 89 ---1 ---89 90 ---1 ---2 ---3 ---5 ---6 ---9 ---10 ---15 ---18 ---30 ---45 ---90 91 ---1 ---7 ---13 ---91 92 ---1 ---2 ---4 ---23 ---46 ---92 93 ---1 ---3 ---31 ---93 94 ---1 ---2 ---47 ---94 95 ---1 ---5 ---19 ---95 96 ---1 ---2 ---3 ---4 ---6 ---8 ---12 ---16 ---24 ---32 ---48 ---96 97 ---1 ---97 98 ---1 ---2 ---7 ---14 ---49 ---98 99 ---1 ---3 ---9 ---11 ---33 ---99 100 ---1 ---2 ---4 ---5 ---10 ---20 ---25 ---50 ---100