# Check if all the elements can be made equal on dividing with X and Y

• Difficulty Level : Medium
• Last Updated : 06 Sep, 2021

Given an array arr[] and two integers X and Y. The task is to check whether it is possible to make all the elements equal by dividing them with X and Y any number of times including 0.

Examples:

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Input: arr[] = {2, 4, 6, 8}, X = 2, Y = 3
Output: Yes
2 -> 2
4 -> (4 / X) = (4 / 2) = 2
6 -> (6 / Y) = (6 / 3) = 2
8 -> (8 / X) = (8 / 2) = 4 and 4 -> (4 / X) = (4 / 2) = 2

Input: arr[] = {2, 4, 10}, X = 11, Y = 12
Output: No

Approach: Find the gcd of all the elements from the given array because this gcd is the value which can we get by dividing all the elements with some arbitrary constants say gcd = arr[0] / k1 or arr[1] / k2 or … or arr[n-1] / kn. Now the task is to find whether these constants k1, k2, k3, …, kn are of the form X * X * X * … * Y Y Y * ….. If yes then it is possible to make all the elements equal with the given operation else it isn’t.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function that returns true if num``// is of the form x*x*x*...*y*y*...``bool` `isDivisible(``int` `num, ``int` `x, ``int` `y)``{` `    ``// While num divisible is divible``    ``// by either x or y, keep dividing``    ``while` `(num % x == 0 || num % y == 0) {``        ``if` `(num % x == 0)``            ``num /= x;``        ``if` `(num % y == 0)``            ``num /= y;``    ``}` `    ``// If num > 1, it means it cannot be``    ``// further divided by either x or y``    ``if` `(num > 1)``        ``return` `false``;` `    ``return` `true``;``}` `// Function that returns true if all``// the array elements can be made``// equal with the given operation``bool` `isPossible(``int` `arr[], ``int` `n, ``int` `x, ``int` `y)``{` `    ``// To store the gcd of the array elements``    ``int` `gcd = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``        ``gcd = __gcd(gcd, arr[i]);` `    ``// For every element of the array``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Check if k is of the form x*x*..*y*y*...``        ``// where (gcd * k = arr[i])``        ``if` `(!isDivisible(arr[i] / gcd, x, y))``            ``return` `false``;``    ``}``    ``return` `true``;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 2, 4, 6, 8 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``int` `x = 2, y = 3;` `    ``if` `(isPossible(arr, n, x, y))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach` `class` `GFG``{` `    ``// Function that returns true if num``    ``// is of the form x*x*x*...*y*y*...``    ``public` `static` `boolean` `isDivisible(``int` `num, ``int` `x, ``int` `y)``    ``{` `        ``// While num divisible is divible``        ``// by either x or y, keep dividing``        ``while` `(num % x == ``0` `|| num % y == ``0``)``        ``{``            ``if` `(num % x == ``0``)``                ``num /= x;``            ``if` `(num % y == ``0``)``                ``num /= y;``        ``}` `        ``// If num > 1, it means it cannot be``        ``// further divided by either x or y``        ``if` `(num > ``1``)``            ``return` `false``;` `        ``return` `true``;``    ``}` `    ``// Function to calculate gcd of two numbers``    ``// using Euclid's algorithm``    ``public` `static` `int` `_gcd(``int` `a, ``int` `b)``    ``{``        ``while` `(a != b)``        ``{``            ``if` `(a > b)``                ``a = a - b;``            ``else``                ``b = b - a;``        ``}` `        ``return` `a;``    ``}` `    ``// Function that returns true if all``    ``// the array elements can be made``    ``// equal with the given operation``    ``public` `static` `boolean` `isPossible(``int``[] arr, ``int` `n,``                                        ``int` `x, ``int` `y)``    ``{``        ` `        ``// To store the gcd of the array elements``        ``int` `gcd = arr[``0``];``        ``for` `(``int` `i = ``1``; i < n; i++)``            ``gcd = _gcd(gcd, arr[i]);` `        ``// For every element of the array``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{` `            ``// Check if k is of the form x*x*..*y*y*...``            ``// where (gcd * k = arr[i])``            ``if` `(!isDivisible(arr[i] / gcd, x, y))``                ``return` `false``;``        ``}``        ``return` `true``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = { ``2``, ``4``, ``6``, ``8` `};``        ``int` `n = arr.length;``        ``int` `x = ``2``, y = ``3``;``        ``if` `(isPossible(arr, n, x, y))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);``    ``}``}` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 implementation of the approach``from` `math ``import` `gcd as __gcd` `# Function that returns True if num``# is of the form x*x*x*...*y*y*...``def` `isDivisible(num, x, y):` `    ``# While num divisible is divible``    ``# by either x or y, keep dividing``    ``while` `(num ``%` `x ``=``=` `0` `or` `num ``%` `y ``=``=` `0``):``        ``if` `(num ``%` `x ``=``=` `0``):``            ``num ``/``/``=` `x``        ``if` `(num ``%` `y ``=``=` `0``):``            ``num ``/``/``=` `y` `    ``# If num > 1, it means it cannot be``    ``# further divided by either x or y``    ``if` `(num > ``1``):``        ``return` `False` `    ``return` `True` `# Function that returns True if all``# the array elements can be made``# equal with the given operation``def` `isPossible(arr, n, x, y):` `    ``# To store the gcd of the array elements``    ``gcd ``=` `arr[``0``]``    ``for` `i ``in` `range``(``1``,n):``        ``gcd ``=` `__gcd(gcd, arr[i])` `    ``# For every element of the array``    ``for` `i ``in` `range``(n):` `        ``# Check if k is of the form x*x*..*y*y*...``        ``# where (gcd * k = arr[i])``        ``if` `(isDivisible(arr[i] ``/``/` `gcd, x, y) ``=``=` `False``):``            ``return` `False``    ``return` `True`  `# Driver code` `arr ``=` `[``2``, ``4``, ``6``, ``8``]``n ``=` `len``(arr)``x ``=` `2``y ``=` `3` `if` `(isPossible(arr, n, x, y) ``=``=` `True``):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)``    ` `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `    ``// Function that returns true if num``    ``// is of the form x*x*x*...*y*y*...``    ``public` `static` `bool` `isDivisible(``int` `num, ``int` `x, ``int` `y)``    ``{` `        ``// While num divisible is divible``        ``// by either x or y, keep dividing``        ``while` `(num % x == 0 || num % y == 0)``        ``{``            ``if` `(num % x == 0)``                ``num /= x;``            ``if` `(num % y == 0)``                ``num /= y;``        ``}` `        ``// If num > 1, it means it cannot be``        ``// further divided by either x or y``        ``if` `(num > 1)``            ``return` `false``;` `        ``return` `true``;``    ``}` `    ``// Function to calculate gcd of two numbers``    ``// using Euclid's algorithm``    ``public` `static` `int` `_gcd(``int` `a, ``int` `b)``    ``{``        ``while` `(a != b)``        ``{``            ``if` `(a > b)``                ``a = a - b;``            ``else``                ``b = b - a;``        ``}` `        ``return` `a;``    ``}` `    ``// Function that returns true if all``    ``// the array elements can be made``    ``// equal with the given operation``    ``public` `static` `bool` `isPossible(``int``[] arr, ``int` `n,``                                        ``int` `x, ``int` `y)``    ``{``        ` `        ``// To store the gcd of the array elements``        ``int` `gcd = arr[0];``        ``for` `(``int` `i = 1; i < n; i++)``            ``gcd = _gcd(gcd, arr[i]);` `        ``// For every element of the array``        ``for` `(``int` `i = 0; i < n; i++)``        ``{` `            ``// Check if k is of the form x*x*..*y*y*...``            ``// where (gcd * k = arr[i])``            ``if` `(!isDivisible(arr[i] / gcd, x, y))``                ``return` `false``;``        ``}``        ``return` `true``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 2, 4, 6, 8 };``        ``int` `n = arr.Length;``        ``int` `x = 2, y = 3;``        ``if` `(isPossible(arr, n, x, y))``            ``Console.Write(``"Yes"``);``        ``else``            ``Console.Write(``"No"``);``    ``}``}` `// This code is contributed by``// anuj_67..`

## Javascript

 ``
Output:
`Yes`

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