The **Largest prime factor** is a very simple concept. Let's break it down:
* Every number has many different factors. 
* **Factors** are numbers that completely divide a particular number to get zero as a remainder.
* For example, if we look at the number `6`, it has four factors: `1`,`2`,`3`,`6`. However, of these *factors*, `2` and `3` are prime numbers. As `3` is greater than `2`, `3` is said to be the *largest prime factor* of number `6`.


#include <iostream>
using namespace std;

bool is_Prime(int x)
{
  // invalid input
  if (x <= 1)
    return false;

  // process all potential divisors
  for(int i = 2; i <= x / 2; i++) {
      if(x % i == 0) {
         return false;
      }
   }
  // no divisor found, therfore it's a prime number
  return true;
}

int main() {
   // the number we want factors of
   int number = 123;
   // iterate from half of the number to 2 as there can be no factor
   // greater than half of the number. 
   for(int i = number/2; i >= 2; i--)
   {
      //check if number is factor
      if(number % i == 0)
      {
         // check if the factor is also a prime number
         if(is_Prime(i))
          cout<<"Largest prime factor = " << i<<endl; 
          break;
      }
   }
  
   return 0;
}

import java.util.Collections;
class HelloWorld {
   // helper function to check is given number is prime
   static boolean is_Prime(int x) {
   if (x <= 1)
    return false;

  // process all potential divisors
  for(int i = 2; i <= x / 2; i++) {
      if(x % i == 0) {
         return false;
      }
   }

  // no divisor found, therfore it's a prime number
  return true;
}
    public static void main( String args[] ) {
      
   // the number we want factors of  
   int number = 123;
   
   // iterate from  half of the number to 2 as there can be no factor
   // greater than half of the number. 
   for(int i = number/2 ; i >=  2; i--)
   {
      // check if number is a factor
      if(number % i == 0)
      {
         // check if factor is also a prime number
         if(is_Prime(i))
         {
            System.out.println("Largest prime factor = " + i);
            break;
         }
      }
   }
    }
}

Java

def isPrime(x):
    # invalid input
    if x <= 1:
        return False

    # process all potential divisors
    for i in range(2,x):
        if x % i == 0:
            return False 
      
    # no divisor found, therfore it's a prime number
    return True
# the number to we want largest prime factor of
number = 123

# iterate from half of the number to 2 as there can be no factor
# greater than half of the number.
for i in range(number//2, 2, -1 ):
    # check if number is a factor
    if number % i == 0:
        # check if factor is also a prime
        if isPrime(i):
            # add the number to the list
            print ("Largest prime factor = " , i)
            break

       

Python3

 **Explanation:** For any number, we must first find out all the factors associated with it. For example, if we look at the number `123`, we can see that it has two factors: `41` and ,`3`. In the code, we run a loop from `number/2` to `2`.(If we run the reverse loop we will find the largest factor first without the hassle to check the smaller ones first). In this case, the loop will run from `61` to `2`. Now, we will check if this `i` is a factor of the given number. If it is a factor then we will check each factor is also a prime number. We have defined a helper function in the code to check if a number is prime or not -- we call this function on every factor. If the number is a factor and also a prime, we add it to the maintained list of factors. At last, we find out the maximum number from the list to obtain the *largest prime factor*.  

java.tar.gz

Largest prime factor 

Find all factors of a number, identify which are prime, and the largest prime factor. For example: 6 → largest prime factor is 3.

Largest prime factor

Code