# Check if it is possible to make array equal by doubling or tripling

Given an array of n elements.You can double or triple the elements in the array any number of times. After all the operations check whether it is possible to make all elements in the array equal.

**Examples :**

Input : A[] = {75, 150, 75, 50} Output : Yes Explanation : Here, 75 should be doubled twice and 150 should be doubled once and 50 should be doubled once and tripled once.Then, all the elements will be equal to 300. Input : A[] = {100, 151, 200} Output : No Explanation : No matter what we do all elements in the array could not be equal.

The idea is to repeatedly divide every element by 2 and 3 until the element is divisible. After this step, if all elements become same, then answer is yes.

How does this work? We know that every integer can be expressed as product of prime numbers **2 ^{a}.3^{b}.5^{c}.7^{d}…..**. So, in our problem we can increase a and b by doubling(*2) or tripling(*3). We can make a and b of all elements in the array equal by multiplying with 2 or 3. But the numbers also have other prime numbers in their product representation, we cannot change the powers of them. So to make all numbers equal they should have powers on other prime numbers equal from the beginning. We can check it by dividing all the numbers by two or three as many times as possible. Then all of them should be equal.

## C++

`// C++ program to check if all numbers can` `// be made equal by repeated division of 2` `// and 3` `#include <bits/stdc++.h>` `using` `namespace` `std;` `bool` `canMakeEqual(` `int` `a[], ` `int` `n)` `{` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `// continuously divide every number by 2 ` ` ` `while` `(a[i] % 2 == 0)` ` ` `a[i] = a[i] / 2;` ` ` `// continuously divide every number by 3` ` ` `while` `(a[i] % 3 == 0)` ` ` `a[i] = a[i] / 3;` ` ` `}` ` ` `// Check if all numbers same` ` ` `for` `(` `int` `i = 1; i < n; i++)` ` ` `if` `(a[i] != a[0])` ` ` `return` `false` `;` ` ` `return` `true` `;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `A[] = { 75, 150, 75, 50 };` ` ` `int` `n = ` `sizeof` `(A) / ` `sizeof` `(A[0]);` ` ` `if` `(canMakeEqual(A, n))` ` ` `cout << ` `"Yes"` `;` ` ` `else` ` ` `cout << ` `"No"` `;` ` ` `return` `0;` `}` |

## Java

`// Java program to check if all numbers can` `// be made equal by repeated division of 2` `// and 3` `import` `java.util.*;` `class` `GFG {` `static` `Boolean canMakeEqual(` `int` `a[], ` `int` `n)` `{` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) {` ` ` `// Continuously divide every number by 2` ` ` `while` `(a[i] % ` `2` `== ` `0` `)` ` ` `a[i] = a[i] / ` `2` `;` ` ` `// Continuously divide every number by 3` ` ` `while` `(a[i] % ` `3` `== ` `0` `)` ` ` `a[i] = a[i] / ` `3` `;` ` ` `}` ` ` `// Check if all numbers same` ` ` `for` `(` `int` `i = ` `1` `; i < n; i++)` ` ` `if` `(a[i] != a[` `0` `])` ` ` `return` `false` `;` ` ` `return` `true` `;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `int` `A[] = { ` `75` `, ` `150` `, ` `75` `, ` `50` `};` ` ` `int` `n = A.length;` ` ` `if` `(canMakeEqual(A, n))` ` ` `System.out.print(` `"Yes"` `);` ` ` `else` ` ` `System.out.print(` `"No"` `);` `}` ` ` `}` `// This code is contributed by 'Gitanjali'.` |

## Python3

`# Python3 code to check if all numbers can` `# be made equal by repeated division of 2` `# and 3` `def` `canMakeEqual( a , n ):` ` ` `for` `i ` `in` `range` `(n):` ` ` `# continuously divide every number by 2` ` ` `while` `a[i] ` `%` `2` `=` `=` `0` `:` ` ` `a[i] ` `=` `int` `(a[i] ` `/` `2` `)` ` ` ` ` `# continuously divide every number by 3` ` ` `while` `a[i] ` `%` `3` `=` `=` `0` `:` ` ` `a[i] ` `=` `int` `(a[i] ` `/` `3` `)` ` ` ` ` `# Check if all numbers same` ` ` `for` `i ` `in` `range` `(` `1` `,n):` ` ` `if` `a[i] !` `=` `a[` `0` `]:` ` ` `return` `False` ` ` ` ` `return` `True` ` ` `# Driver Code` `A ` `=` `[ ` `75` `, ` `150` `, ` `75` `, ` `50` `]` `n ` `=` `len` `(A)` `print` `(` `"Yes"` `if` `canMakeEqual(A, n) ` `else` `"No"` `)` `# This code is contributed by "Sharad_Bhardwaj".` |

## C#

`// C# program to check if all numbers can` `// be made equal by repeated division of 2` `// and 3` `using` `System;` `class` `GFG {` ` ` `static` `Boolean canMakeEqual(` `int` `[]a, ` `int` `n)` ` ` `{` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` ` ` `// Continuously divide every number by 2` ` ` `while` `(a[i] % 2 == 0)` ` ` `a[i] = a[i] / 2;` ` ` ` ` `// Continuously divide every number by 3` ` ` `while` `(a[i] % 3 == 0)` ` ` `a[i] = a[i] / 3;` ` ` `}` ` ` ` ` `// Check if all numbers same` ` ` `for` `(` `int` `i = 1; i < n; i++)` ` ` `if` `(a[i] != a[0])` ` ` `return` `false` `;` ` ` ` ` `return` `true` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` ` ` `int` `[]A = { 75, 150, 75, 50 };` ` ` `int` `n = A.Length;` ` ` ` ` `if` `(canMakeEqual(A, n))` ` ` `Console.WriteLine(` `"Yes"` `);` ` ` `else` ` ` `Console.WriteLine(` `"No"` `);` ` ` `}` `}` `// This code is contributed by 'vt_m'.` |

## PHP

`<?php` `// PHP program to check if` `// all numbers can be made` `// equal by repeated division` `// of 2 and 3` `function` `canMakeEqual(` `$a` `, ` `$n` `)` `{` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `{` ` ` `// continuously divide` ` ` `// every number by 2` ` ` `while` `(` `$a` `[` `$i` `] % 2 == 0)` ` ` `$a` `[` `$i` `] = ` `$a` `[` `$i` `] / 2;` ` ` `// continuously divide` ` ` `// every number by 3` ` ` `while` `(` `$a` `[` `$i` `] % 3 == 0)` ` ` `$a` `[` `$i` `] = ` `$a` `[` `$i` `] / 3;` ` ` `}` ` ` `// Check if all numbers same` ` ` `for` `(` `$i` `= 1; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `if` `(` `$a` `[` `$i` `] != ` `$a` `[0])` ` ` `return` `false;` ` ` `return` `true;` `}` `// Driver Code` `$A` `= ` `array` `(75, 150, 75, 50);` `$n` `= sizeof(` `$A` `);` `if` `(canMakeEqual(` `$A` `, ` `$n` `))` ` ` `echo` `"Yes"` `;` `else` ` ` `echo` `"No"` `;` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `// Javascript program to check if all numbers can` `// be made equal by repeated division of 2` `// and 3` `function` `canMakeEqual(a, n)` `{` ` ` `for` `(let i = 0; i < n; i++)` ` ` `{` ` ` ` ` `// Continuously divide every number by 2` ` ` `while` `(a[i] % 2 == 0)` ` ` `a[i] = a[i] / 2;` ` ` ` ` `// Continuously divide every number by 3` ` ` `while` `(a[i] % 3 == 0)` ` ` `a[i] = a[i] / 3;` ` ` `}` ` ` ` ` `// Check if all numbers same` ` ` `for` `(let i = 1; i < n; i++)` ` ` `if` `(a[i] != a[0])` ` ` `return` `false` `;` ` ` ` ` `return` `true` `;` `}` `// Driver code` `let A = [ 75, 150, 75, 50 ];` `let n = A.length;` `if` `(canMakeEqual(A, n))` ` ` `document.write(` `"Yes"` `);` `else` ` ` `document.write(` `"No"` `);` ` ` `// This code is contributed by suresh07` `</script>` |

**Output :**

Yes

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.