# Maximum Factors Problem CodeChef Solution – Code Drive Solution

### About Maximum Factors Problem CodeChef Solution

• This is a coding contest based on algorithms, data structures, and problem-solving.
• Organizer: The contest is hosted by NIT Trichy.
• Prizes: NA
• Registrations for prizes: NA

### Problem: Maximum Factors Problem CodeChef Solution

You are given an integer NN. Let KK be a divisor of NN of your choice such that K>1K>1, and let M=NKM=NK. You need to find the smallest KK such that MM has as many divisors as possible.

Note: UU is a divisor of VV if VV is divisible by UU.

### Input Format

• The first line of the input contains an integer TT – the number of test cases. The test cases then follow.
• The only line of each test case contains an integer NN.

### Output Format

For each test case, output in a single line minimum value of KK such that MM has as many divisors as possible.

### Constraints

• 1≤T≤30001≤T≤3000
• 2≤N≤1092≤N≤109

### Sample Input 1

``````3
3
4
6
``````

### Sample Output 1

``````3
2
2
``````

### Explanation

• Test case 11: The only possible value for KK is 33, and that is the answer.
• Test case 22: There are two cases:
• K=2K=2. Then M=42=2M=42=2, which has 22 divisors (11 and 22).
• K=4K=4. Then M=44=1M=44=1, which has 11 divisor (11).

• Test case 33: There are three cases:
• K=2K=2. Then M=62=3M=62=3, which has 22 divisors (11 and 33).
• K=3K=3. Then M=63=2M=63=2, which has 22 divisors (11 and 22).
• K=6K=6. Then M=66=1M=66=1, which has 11 divisor (11).

#### Contest Details:

• This is an External Rated Contest.
• Duration: 3 Hours
• Start time: 30th December 2021, 20:00 hrs IST
• End time: 30th December 2021, 23:00 hrs IST
You may check your timezone here.
• This contest is rated only for Division 2 and Division 3 users. Division 1 users can participate unofficially in this contest.

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