# Factor Combinations

Moderate
0/80
Average time to solve is 35m
Contributed by

## Problem statement

You are given a positive integer ‘N’. Find all the unique combinations of factors of the given number ‘N’. The product of the factors in each combination should be ‘N’.

You should return a list of combinations of factors. In each combination, factors must be sorted in non-decreasing order. All combinations must be placed in lexicographical order in the list. See the example for more clarity.

Note

``````1. Factors should be strictly greater than 1 and strictly less than ‘N’.

2. If there is no such possible combination of factors, then return an empty list.
``````

Example:

``````Consider the positive integer ‘N’ = 12.
Then, we can observe that -:
12 = 2 * 2 * 3
12 = 2 * 6
12 = 3 * 4

i.e,  possible combinations of factors are [2, 2, 3], [2, 6], [3, 4].
Thus, we should return list [[2,2,3], [2,6], [3, 4]].  Note that in this list all combinations are sorted in non-decreasing order, and all the combinations in the list are placed in the lexicographical order.
``````
Detailed explanation ( Input/output format, Notes, Images )
Constraints:
``````1 <= T <= 50
2 <= N <= 1000

Where ‘T’ is the total number of test cases, and  ‘N’ is the given integer.

Time limit: 1 sec
``````
##### Sample Input 1:
``````2
5
12
``````
##### Sample Output 1:
``````0
3
2 2 3
2 6
3 4
``````
##### Explanation of Sample Input 1:
``````Test case 1:
The integer 5 is a prime number, and it has no factors. Note, we consider that factors should be strictly greater than 1 and strictly less than ‘N’.

Test case 2:
See the problem statement for an explanation.
``````
##### Sample Input 2:
``````2
16
4
``````
##### Sample Output 2:
``````4
2 2 2 2
2 2 4
2 8
4 4
1
2 2
``````
Console