Tuesday, January 8, 2013

Problem 12: Highly divisible triangular number


The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
 1: 1
 3: 1,3
 6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?

Solution:
java code:


public class Prob12 {

 
 public static void main(String[] args) {
  int DivCount =0;
  long i =76576499;
  while (DivCount <= 500)
  { i++;
   if(CheckTriangular(i))
    {
    DivCount=divisorCount(i);
   
    }
   
  
  }
  System.out.println(i);

 }
public static boolean CheckTriangular(long a)
{
long A81= 8*a+1;
long sqrt =(long)Math.sqrt(A81);
if (sqrt*sqrt == A81)
return true; 
else
return false;

}
public static int divisorCount(long a)
{
 int count =0;
 for(long i = 1; i <= a; i++ )
 {
  if(a%i ==0)
  count++;
 }
 return count;
 }

}

1 comment:

  1. why did u take i=76576499?
    n why u took A81=8*a+1?
    pls explain the logic...
    by the way ur programs r very easy to understand for a begineer like me...
    thnx a lot..

    ReplyDelete