# Find distinct integers for a triplet with given product

Given an integer X, the task is to find the three distinct integers greater than 1 i.e. A, B and C such that (A * B * C) = X. If no such triplet exists then print -1.

Examples:

Input: X = 64
Output: 2 4 8
(2 * 4 * 8) = 64

Input: X = 32
Output: -1
No such triplet exists.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Suppose we have a triplet (A, B, C). Notice that, for their product to be equal to X, each of the integer has to be a factor of X. So, store all the factors of X in O(sqrt(X)) time using the approach discussed in this article.
There will be at most sqrt(X) factors now. Next, iterate on each factor by running two loops, one picking A and another picking B. Now if this triplet is valid i.e. C = X / (A * B) where C is also a factor of X. To check that, store all the factors in an unordered_set. If a valid triplet is found then print the triplet else print -1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the required triplets ` `void` `findTriplets(``int` `x) ` `{ ` `    ``// To store the factors ` `    ``vector<``int``> fact; ` `    ``unordered_set<``int``> factors; ` ` `  `    ``// Find factors in sqrt(x) time ` `    ``for` `(``int` `i = 2; i <= ``sqrt``(x); i++) { ` `        ``if` `(x % i == 0) { ` `            ``fact.push_back(i); ` `            ``if` `(x / i != i) ` `                ``fact.push_back(x / i); ` `            ``factors.insert(i); ` `            ``factors.insert(x / i); ` `        ``} ` `    ``} ` ` `  `    ``bool` `found = ``false``; ` `    ``int` `k = fact.size(); ` `    ``for` `(``int` `i = 0; i < k; i++) { ` ` `  `        ``// Choose a factor ` `        ``int` `a = fact[i]; ` `        ``for` `(``int` `j = 0; j < k; j++) { ` ` `  `            ``// Choose another factor ` `            ``int` `b = fact[j]; ` ` `  `            ``// These conditions need to be ` `            ``// met for a valid triplet ` `            ``if` `((a != b) && (x % (a * b) == 0) ` `                ``&& (x / (a * b) != a) ` `                ``&& (x / (a * b) != b) ` `                ``&& (x / (a * b) != 1)) { ` ` `  `                ``// Print the valid triplet ` `                ``cout << a << ``" "` `<< b << ``" "` `                     ``<< (x / (a * b)); ` `                ``found = ``true``; ` `                ``break``; ` `            ``} ` `        ``} ` ` `  `        ``// Triplet found ` `        ``if` `(found) ` `            ``break``; ` `    ``} ` ` `  `    ``// Triplet not found ` `    ``if` `(!found) ` `        ``cout << ``"-1"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `x = 105; ` ` `  `    ``findTriplets(x); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the required triplets ` `static` `void` `findTriplets(``int` `x) ` `{ ` `    ``// To store the factors ` `    ``Vector fact = ``new` `Vector(); ` `    ``HashSet factors = ``new` `HashSet(); ` ` `  `    ``// Find factors in Math.sqrt(x) time ` `    ``for` `(``int` `i = ``2``; i <= Math.sqrt(x); i++)  ` `    ``{ ` `        ``if` `(x % i == ``0``)  ` `        ``{ ` `            ``fact.add(i); ` `            ``if` `(x / i != i) ` `                ``fact.add(x / i); ` `            ``factors.add(i); ` `            ``factors.add(x / i); ` `        ``} ` `    ``} ` ` `  `    ``boolean` `found = ``false``; ` `    ``int` `k = fact.size(); ` `    ``for` `(``int` `i = ``0``; i < k; i++) ` `    ``{ ` ` `  `        ``// Choose a factor ` `        ``int` `a = fact.get(i); ` `        ``for` `(``int` `j = ``0``; j < k; j++)  ` `        ``{ ` ` `  `            ``// Choose another factor ` `            ``int` `b = fact.get(j); ` ` `  `            ``// These conditions need to be ` `            ``// met for a valid triplet ` `            ``if` `((a != b) && (x % (a * b) == ``0``) ` `                ``&& (x / (a * b) != a) ` `                ``&& (x / (a * b) != b) ` `                ``&& (x / (a * b) != ``1``))  ` `            ``{ ` ` `  `                ``// Print the valid triplet ` `                ``System.out.print(a+ ``" "` `+ b + ``" "` `                    ``+ (x / (a * b))); ` `                ``found = ``true``; ` `                ``break``; ` `            ``} ` `        ``} ` ` `  `        ``// Triplet found ` `        ``if` `(found) ` `            ``break``; ` `    ``} ` ` `  `    ``// Triplet not found ` `    ``if` `(!found) ` `        ``System.out.print(``"-1"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `x = ``105``; ` ` `  `    ``findTriplets(x); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 implementation of the approach  ` `from` `math ``import` `sqrt ` ` `  `# Function to find the required triplets  ` `def` `findTriplets(x) :  ` ` `  `    ``# To store the factors  ` `    ``fact ``=` `[];  ` `    ``factors ``=` `set``();  ` ` `  `    ``# Find factors in sqrt(x) time  ` `    ``for` `i ``in` `range``(``2``, ``int``(sqrt(x))) : ` `        ``if` `(x ``%` `i ``=``=` `0``) : ` `            ``fact.append(i);  ` `             `  `            ``if` `(x ``/` `i !``=` `i) : ` `                ``fact.append(x ``/``/` `i);  ` `                 `  `            ``factors.add(i);  ` `            ``factors.add(x ``/``/` `i);  ` ` `  `    ``found ``=` `False``;  ` `    ``k ``=` `len``(fact);  ` `     `  `    ``for` `i ``in` `range``(k) : ` ` `  `        ``# Choose a factor  ` `        ``a ``=` `fact[i];  ` `         `  `        ``for` `j ``in` `range``(k) : ` ` `  `            ``# Choose another factor  ` `            ``b ``=` `fact[j];  ` ` `  `            ``# These conditions need to be  ` `            ``# met for a valid triplet  ` `            ``if` `((a !``=` `b) ``and` `(x ``%` `(a ``*` `b) ``=``=` `0``)  ` `                ``and` `(x ``/` `(a ``*` `b) !``=` `a)  ` `                ``and` `(x ``/` `(a ``*` `b) !``=` `b)  ` `                ``and` `(x ``/` `(a ``*` `b) !``=` `1``)) : ` ` `  `                ``# Print the valid triplet  ` `                ``print``(a,b,x ``/``/` `(a ``*` `b));  ` `                ``found ``=` `True``;  ` `                ``break``;  ` `     `  `        ``# Triplet found  ` `        ``if` `(found) : ` `            ``break``;  ` ` `  `    ``# Triplet not found  ` `    ``if` `(``not` `found) :  ` `        ``print``(``"-1"``);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``x ``=` `105``;  ` ` `  `    ``findTriplets(x);  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the required triplets ` `static` `void` `findTriplets(``int` `x) ` `{ ` `    ``// To store the factors ` `    ``List<``int``> fact = ``new` `List<``int``>(); ` `    ``HashSet<``int``> factors = ``new` `HashSet<``int``>(); ` ` `  `    ``// Find factors in Math.Sqrt(x) time ` `    ``for` `(``int` `i = 2; i <= Math.Sqrt(x); i++)  ` `    ``{ ` `        ``if` `(x % i == 0)  ` `        ``{ ` `            ``fact.Add(i); ` `            ``if` `(x / i != i) ` `                ``fact.Add(x / i); ` `            ``factors.Add(i); ` `            ``factors.Add(x / i); ` `        ``} ` `    ``} ` ` `  `    ``bool` `found = ``false``; ` `    ``int` `k = fact.Count; ` `    ``for` `(``int` `i = 0; i < k; i++) ` `    ``{ ` ` `  `        ``// Choose a factor ` `        ``int` `a = fact[i]; ` `        ``for` `(``int` `j = 0; j < k; j++)  ` `        ``{ ` ` `  `            ``// Choose another factor ` `            ``int` `b = fact[j]; ` ` `  `            ``// These conditions need to be ` `            ``// met for a valid triplet ` `            ``if` `((a != b) && (x % (a * b) == 0) ` `                ``&& (x / (a * b) != a) ` `                ``&& (x / (a * b) != b) ` `                ``&& (x / (a * b) != 1))  ` `            ``{ ` ` `  `                ``// Print the valid triplet ` `                ``Console.Write(a+ ``" "` `+ b + ``" "` `                    ``+ (x / (a * b))); ` `                ``found = ``true``; ` `                ``break``; ` `            ``} ` `        ``} ` ` `  `        ``// Triplet found ` `        ``if` `(found) ` `            ``break``; ` `    ``} ` ` `  `    ``// Triplet not found ` `    ``if` `(!found) ` `        ``Console.Write(``"-1"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `x = 105; ` ` `  `    ``findTriplets(x); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```3 5 7
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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