1730: 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.