Many thanks to Clive Fraser aka CSFPython for creating this puzzle!
You are given a positive integer N and must find 3 positive integers X, Y and Z which satisfy all of
the following conditions.
3 numbers X, Y and Z are all different and are all greater than 1.X*Y, X*Z and Y*Z are all divisors of N.X*Y*Z is a multiple of N.For example, if N = 100 we find that X = 2, Y = 5 and Z = 10 satisfies these 3 conditions.
The products X*Y, X*Z and Y*Z are 10, 20 and 50 respectively. All of these are divisors of
N = 100. The product X*Y*Z = 2*5*10 = 100 = 1 x 100. So this is a multiple of N as required.
If we consider N = 35 we soon find that there is no combination of integers X, Y and Z which satisfy
the requirements.
For each solution you must give the 3 values of X, Y and Z in ascending size order,
separated by single spaces. If there is no solution for a particular value of N, you indicate this with a
single 0 in place of the 3 values for X, Y and Z.
Input/Output description: The first line of the input data will contain a single integer M,
the number of different values of N to consider. M lines will follow. Each line contains a single value of N.
Find the corresponding values of X, Y and Z (in ascending order) or report 0 if there is no solution.
Combine all answers into a single string, separated by spaces.
Example:
input:
3
100
35
3485
answer:
2 5 10 0 5 17 41