title: Largest Prime Factor- C++
body: <p>I'm trying to find the largest prime factor of the number 600851475143. My code works for smaller numbers that I test (below 100). However when confronted with 600851475143, it returns 4370432, definitely not prime. Any ideas what could be wrong with my code?</p>
  
  <pre><code>#include &lt;iostream&gt;
  #include &lt;time.h&gt;
  #include &lt;math.h&gt;
  
  using namespace std;
  
  int main()
  {
  
  int num;
  int largest;
  int count;
  
  cout&lt;&lt;"Please enter a number to have its Largest Prime Factor found"&lt;&lt;endl;
  cin&gt;&gt;num;
  num = 600851475143;
  
  for (int factor = 1; factor &lt;= num; factor++)
  {
      if (num % factor == 0)
      {
          count = 0;
          for (int primetest=2; count == 0 &amp;&amp; factor &gt; primetest ; primetest++) 
          {
              if (factor % primetest == 0)
              count ++;    
              //endif
          }
          if (count == 0)
          largest = factor;
          //endif
      }       
  
  }//endif
  cout&lt;&lt;largest&lt;&lt;endl;
  system("PAUSE");
  }
  </code></pre>