Check if N can be expressed as product of 3 distinct numbers


Given a number N. Print three distinct numbers (>=1) whose product is equal to N. print -1 if it is not possible to find three numbers.

Examples:

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

Input: 24
Output: 2 3 4
Explanation:
(2*3*4 = 24)

Input: 12
Output: -1
Explanation:
No such triplet exists



Approach:

  1. Make an array which stores all the divisors of the given number using the approach discussed in this article
  2. Let the three number be a, b, c initialize to 1
  3. Traverse the divisors array and check the following condition:
    • value of a = value at 1st index of divisor array.
    • value of b = product of value at 2nd and 3rd index of divisor array. If divisor array has only one or two element then no such triplets exists
    • After finding a & b, value of c = product of all the rest elements in divisor array.
  4. Check the final condition such that value of a, b, c must be distinct and not equal to 1.

Below is the implementation code:

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// C++ program to find the
// three numbers
#include "bits/stdc++.h"
using namespace std;
  
// function to find 3 distinct number
// with given product
void getnumbers(int n)
{
    // Declare a vector to store
    // divisors
    vector<int> divisor;
  
    // store all divisors of number
    // in array
    for (int i = 2; i * i <= n; i++) {
  
        // store all the occurence of
        // divisors
        while (n % i == 0) {
            divisor.push_back(i);
            n /= i;
        }
    }
  
    // check if n is not equals to -1
    // then n is also a prime factor
    if (n != 1) {
        divisor.push_back(n);
    }
  
    // Initialize the variables with 1
    int a, b, c, size;
    a = b = c = 1;
    size = divisor.size();
  
    for (int i = 0; i < size; i++) {
  
        // check for first number a
        if (a == 1) {
            a = a * divisor[i];
        }
  
        // check for second number b
        else if (b == 1 || b == a) {
            b = b * divisor[i];
        }
  
        // check for third number c
        else {
            c = c * divisor[i];
        }
    }
  
    // check for all unwanted codition
    if (a == 1 || b == 1 || c == 1
        || a == b || b == c || a == c) {
        cout << "-1" << endl;
    }
    else {
        cout << a << ' ' << b
             << ' ' << c << endl;
    }
}
  
// Driver function
int main()
{
    int n = 64;
    getnumbers(n);
}
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// Java program to find the
// three numbers
import java.util.*;
  
class GFG{
   
// function to find 3 distinct number
// with given product
static void getnumbers(int n)
{
    // Declare a vector to store
    // divisors
    Vector<Integer> divisor = new Vector<Integer>();
   
    // store all divisors of number
    // in array
    for (int i = 2; i * i <= n; i++) {
   
        // store all the occurence of
        // divisors
        while (n % i == 0) {
            divisor.add(i);
            n /= i;
        }
    }
   
    // check if n is not equals to -1
    // then n is also a prime factor
    if (n != 1) {
        divisor.add(n);
    }
   
    // Initialize the variables with 1
    int a, b, c, size;
    a = b = c = 1;
    size = divisor.size();
   
    for (int i = 0; i < size; i++) {
   
        // check for first number a
        if (a == 1) {
            a = a * divisor.get(i);
        }
   
        // check for second number b
        else if (b == 1 || b == a) {
            b = b * divisor.get(i);
        }
   
        // check for third number c
        else {
            c = c * divisor.get(i);
        }
    }
   
    // check for all unwanted codition
    if (a == 1 || b == 1 || c == 1
        || a == b || b == c || a == c) {
        System.out.print("-1" +"\n");
    }
    else {
        System.out.print(a +" "+ b
                +" "+ c +"\n");
    }
}
   
// Driver function
public static void main(String[] args)
{
    int n = 64;
    getnumbers(n);
}
}
  
// This code is contributed by sapnasingh4991
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# Python3 program to find the
# three numbers
  
# function to find 3 distinct number
# with given product
def getnumbers(n):
       
     # Declare a vector to store
    # divisors
    divisor = []
  
    # store all divisors of number
    # in array
    for i in range(2, n + 1):
  
        # store all the occurence of
        # divisors
        while (n % i == 0):
            divisor.append(i)
            n //= i
  
    # check if n is not equals to -1
    # then n is also a prime factor
    if (n != 1):
        divisor.append(n)
  
    # Initialize the variables with 1
    a, b, c, size = 0, 0, 0, 0
    a = b = c = 1
    size = len(divisor)
  
    for i in range(size):
  
        # check for first number a
        if (a == 1):
            a = a * divisor[i]
  
        # check for second number b
        elif (b == 1 or b == a):
            b = b * divisor[i]
  
        # check for third number c
        else:
            c = c * divisor[i]
  
    # check for all unwanted codition
    if (a == 1 or b == 1 or c == 1
        or a == b or b == c or a == c):
        print("-1")
    else:
        print(a, b, c)
  
# Driver function
  
n = 64
getnumbers(n)
  
# This code is contributed by mohit kumar 29
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// C# program to find the
// three numbers
using System;
using System.Collections.Generic;
  
class GFG{
    
// function to find 3 distinct number
// with given product
static void getnumbers(int n)
{
    // Declare a vector to store
    // divisors
    List<int> divisor = new List<int>();
    
    // store all divisors of number
    // in array
    for (int i = 2; i * i <= n; i++) {
    
        // store all the occurence of
        // divisors
        while (n % i == 0) {
            divisor.Add(i);
            n /= i;
        }
    }
    
    // check if n is not equals to -1
    // then n is also a prime factor
    if (n != 1) {
        divisor.Add(n);
    }
    
    // Initialize the variables with 1
    int a, b, c, size;
    a = b = c = 1;
    size = divisor.Count;
    
    for (int i = 0; i < size; i++) {
    
        // check for first number a
        if (a == 1) {
            a = a * divisor[i];
        }
    
        // check for second number b
        else if (b == 1 || b == a) {
            b = b * divisor[i];
        }
    
        // check for third number c
        else {
            c = c * divisor[i];
        }
    }
    
    // check for all unwanted codition
    if (a == 1 || b == 1 || c == 1
        || a == b || b == c || a == c) {
        Console.Write("-1" +"\n");
    }
    else {
        Console.Write(a +" "+ b
                +" "+ c +"\n");
    }
}
    
// Driver function
public static void Main(String[] args)
{
    int n = 64;
    getnumbers(n);
}
}
  
// This code is contributed by Rajput-Ji
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Output:
2 4 8

Time Complexity: O((log N)*sqrt(N))

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