2013
11-12

# Max Factor

To improve the organization of his farm, Farmer John labels each of his N (1 <= N <= 5,000) cows with a distinct serial number in the range 1..20,000. Unfortunately, he is unaware that the cows interpret some serial numbers as better than others. In particular, a cow whose serial number has the highest prime factor enjoys the highest social standing among all the other cows.

(Recall that a prime number is just a number that has no divisors except for 1 and itself. The number 7 is prime while the number 6, being divisible by 2 and 3, is not).

Given a set of N (1 <= N <= 5,000) serial numbers in the range 1..20,000, determine the one that has the largest prime factor.

* Line 1: A single integer, N

* Lines 2..N+1: The serial numbers to be tested, one per line

* Line 1: The integer with the largest prime factor. If there are more than one, output the one that appears earliest in the input file.

4
36
38
40
42

38

OUTPUT DETAILS:

19 is a prime factor of 38. No other input number has a larger prime factor.

/* @author: */
import java.util.Scanner;
import java.util.Arrays;
public class Main{

public static void main(String args[])
{
Scanner sc=new Scanner(System.in);

int n,mx=-1,tag=-1,i,v;
n=sc.nextInt();
while((n--)!=0)
{
v=sc.nextInt();
int u=v;
int maxx=1;
if(v%2==0)
{
maxx=2;
while(v%2==0)v/=2;
}
for(i=3;i*i<=v;i+=2)
{
if(v%i==0)
{
maxx=i;
while(v%i==0)v/=i;
}
}
if(v>maxx)maxx=v;
if(maxx>mx)
{
mx=maxx;
tag=u;
}
}
System.out.printf("%d\n",tag);
}
}

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