Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 80

Question

I get an error Exception in thread "main"

java.lang.ArrayIndexOutOfBoundsException: 80 at Factorial.fact<Factorial.java:32> and at <Factorial.main.java:5>

I'm not sure how to fix this program?

class Factorial
{
   public static void main(String[] args)
   {
     int[] a=fact(0);
     int[] b=fact(1);
     int[] c=fact(5);
     int[] d=fact(50);   
     System.out.println("zero factorial  = ");   
     for(int i=0;i<a.length;i++)
        System.out.println(fact(i));
     System.out.println("one factorial   = ");
     for(int j=0;j<b.length;j++)
        System.out.println(fact(j));
     System.out.println("five factorial  = ");
     for(int k=0;k<c.length;k++)
        System.out.println(fact(k));
     System.out.println("fifty factorial = ");
     for(int l=0;l<d.length;l++)
        System.out.println(fact(l));
  }
  public static int[] fact(int n)
  {
     int[] product=new int[80];
     for(int a=1; a<product.length;a++)
        product[a]=0;
     product[0]=1;
     for(int b=2,c=0; b<=n;b++,c++)
        product[c]=product[c]*b;
     for(int d=0;d<product.length;d++)
     {
        product[d+1]=product[d+1]+(product[d]/10);
        product[d]=product[d]%10;
     }
     return product;
  }
}

Answer 1

What's going to happen here:

 for(int d=0;d<product.length;d++)
 {
    product[d+1]=product[d+1]+(product[d]/10);
    product[d]=product[d]%10;
 }

when d == product.length - 1? specifically here product[d+1]

An index out of bounds error since here d + 1 is beyond the allowed indexes for the product array.