A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The prime factors of a number are all of the prime numbers that will exactly divide the given number.

For example-

Prime factor of 15 = 3,5

Prime factor of 48=2,2,2,2,3Lets create java program for it:

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package org.arpit.java2blog; import java.util.ArrayList; import java.util.List; public class PrimeFactorsMain { // This method calculate prime factor and add it to primeFactor list public static List primeFactors(int number) { int n = number; List primeFactors = new ArrayList(); for (int i = 2; i <= n; i++) { while (n % i == 0) { primeFactors.add(i); n /= i; } } return primeFactors; } public static void main(String[] args) { System.out.println("Primefactors of 15 are : "); System.out.printf("%s %n",primeFactors(15)); System.out.println("Primefactors of 48 are :"); System.out.printf("%s %n",primeFactors(48)); System.out.println("Primefactors of 91"); System.out.printf("%s %n",primeFactors(91)); } } |

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Primefactors of 15 are : [3, 5] Primefactors of 48 are : [2, 2, 2, 2, 3] Primefactors of 91 [7, 13] |

#### More optimized solution:

Change above primeFactors function to below function

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// This method calculate prime factor and add it to primeFactor list public static List primeFactors(int number) { int n = number; List primeFactors = new ArrayList(); for (int i = 2; i <= n/i; i++) { while (n % i == 0) { primeFactors.add(i); n /= i; } } if(n>1) primeFactors.add(n); return primeFactors; } |

This is based on the fact that in above for loop,divisor can not be greater than n/i.

Please go through java interview programs for more such programs.

Further optimization can be done by running this loop till square root of input number.