Number of squares of maximum area in a rectangle

Given a rectangle of sides m and n. Cut the rectangle into smaller identical pieces such that each piece is a square having maximum possible side length with no leftover part of the rectangle. Print number of such squares formed.
Examples:

```Input: 9 6
Output: 6
Rectangle can be cut into squares of size 3.

Input: 4 2
Output: 2
Rectangle can be cut into squares of size 2.```

Approach: The task is to cut the rectangle in squares with the side of length s without pieces of the rectangle left over, so s must divide both m and n. Also, the side of the square should be maximum possible, therefore, s should be the greatest common divisor of m and n.
so, s = gcd(m, n)
To find the number of squares the rectangle is cut into, the task to be done is to divide the area of a rectangle with an area of the square of size s.

C++

 `// C++ code for calculating the` `// number of squares` `#include ` `using` `namespace` `std;`   `// Function to find number of squares` `int` `NumberOfSquares(``int` `x, ``int` `y)` `{` `    ``// Here in built c++ gcd function is used` `    ``int` `s = __gcd(x, y);`   `    ``int` `ans = (x * y) / (s * s);`   `    ``return` `ans;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `m = 385, n = 60;`   `    ``// Call the function NumberOfSquares` `    ``cout << NumberOfSquares(m, n);`   `    ``return` `0;` `}`

C

 `// C code for calculating the` `// number of squares` `#include `   `int` `gcd(``int` `a, ``int` `b)` `{` `   ``int` `gcd = 1;` `   ``for``(``int` `i = 1; i <= a && i <= b; i++)  ` `    ``{  ` `        ``if` `(a % i ==0 && b % i == 0)  ` `            ``gcd = i;` `    ``}` `    ``return` `gcd;` `}`   `// Function to find number of squares` `int` `NumberOfSquares(``int` `x, ``int` `y)` `{` `    ``// Here in built c++ gcd function is used` `    ``int` `s = gcd(x, y);`   `    ``int` `ans = (x * y) / (s * s);`   `    ``return` `ans;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `m = 385, n = 60;`   `    ``// Call the function NumberOfSquares` `    ``printf``(``"%d"``,NumberOfSquares(m, n));`   `    ``return` `0;` `}`   `// This code is contributed by kothavvsaakash.`

Java

 `// Java code for calculating ` `// the number of squares` `import` `java.io.*;`   `class` `GFG` `{` `    ``// Recursive function to` `    ``// return gcd of a and b` `    ``static` `int` `__gcd(``int` `a, ``int` `b)` `    ``{` `        ``// Everything divides 0 ` `        ``if` `(a == ``0` `|| b == ``0``)` `        ``return` `0``;` `    `  `        ``// base case` `        ``if` `(a == b)` `            ``return` `a;` `    `  `        ``// a is greater` `        ``if` `(a > b)` `            ``return` `__gcd(a - b, b);` `        ``return` `__gcd(a, b - a);` `    ``} `     `// Function to find ` `// number of squares` `static` `int` `NumberOfSquares(``int` `x, ` `                           ``int` `y)` `{` `    ``// Here in built c++ ` `    ``// gcd function is used` `    ``int` `s = __gcd(x, y);`   `    ``int` `ans = (x * y) / (s * s);`   `    ``return` `ans;` `}`   `// Driver Code` `public` `static` `void` `main (String[] args) ` `{` `    ``int` `m = ``385``, n = ``60``;`   `    ``// Call the function` `    ``// NumberOfSquares` `    ``System.out.println(NumberOfSquares(m, n));` `}` `}`   `// This code is contributed by anuj_67.`

Python3

 `# Python3 code for calculating ` `# the number of squares`   `# Recursive function to` `# return gcd of a and b` `def` `__gcd(a, b):` `    `  `    ``# Everything divides 0 ` `    ``if` `(a ``=``=` `0` `or` `b ``=``=` `0``):` `        ``return` `0``;`   `    ``# base case` `    ``if` `(a ``=``=` `b):` `        ``return` `a;`   `    ``# a is greater` `    ``if` `(a > b):` `        ``return` `__gcd(a ``-` `b, b);` `    ``return` `__gcd(a, b ``-` `a);`   `# Function to find ` `# number of squares` `def` `NumberOfSquares(x, y):` `    `  `    ``# Here in built PHP` `    ``# gcd function is used` `    ``s ``=` `__gcd(x, y);`   `    ``ans ``=` `(x ``*` `y) ``/` `(s ``*` `s);`   `    ``return` `int``(ans);`   `# Driver Code` `m ``=` `385``;` `n ``=` `60``;`   `# Call the function` `# NumberOfSquares` `print``(NumberOfSquares(m, n));`   `# This code is contributed ` `# by mit`

C#

 `// C# code for calculating ` `// the number of squares` `using` `System;`   `class` `GFG` `{` `    `  `    ``// Recursive function to` `    ``// return gcd of a and b` `    ``static` `int` `__gcd(``int` `a, ``int` `b)` `    ``{` `        ``// Everything divides 0 ` `        ``if` `(a == 0 || b == 0)` `        ``return` `0;` `    `  `        ``// base case` `        ``if` `(a == b)` `            ``return` `a;` `    `  `        ``// a is greater` `        ``if` `(a > b)` `            ``return` `__gcd(a - b, b);` `        ``return` `__gcd(a, b - a);` `    ``} `     `// Function to find ` `// number of squares` `static` `int` `NumberOfSquares(``int` `x, ` `                           ``int` `y)` `{` `    ``// Here in built c++ ` `    ``// gcd function is used` `    ``int` `s = __gcd(x, y);`   `    ``int` `ans = (x * y) / ` `              ``(s * s);`   `    ``return` `ans;` `}`   `// Driver Code` `static` `public` `void` `Main ()` `{` `int` `m = 385, n = 60;`   `// Call the function` `// NumberOfSquares` `Console.WriteLine(NumberOfSquares(m, n));` `}` `}`   `// This code is contributed by ajit`

PHP

 ` ``\$b``)` `        ``return` `__gcd(``\$a` `- ``\$b``, ``\$b``);` `    ``return` `__gcd(``\$a``, ``\$b` `- ``\$a``);` `} `   `// Function to find ` `// number of squares` `function` `NumberOfSquares(``\$x``, ``\$y``) ` `{` `    ``// Here in built PHP` `    ``// gcd function is used` `    ``\$s` `= __gcd(``\$x``, ``\$y``);`   `    ``\$ans` `= (``\$x` `* ``\$y``) / ` `           ``(``\$s` `* ``\$s``);`   `    ``return` `\$ans``;` `}`   `// Driver Code` `\$m` `= 385;` `\$n` `= 60;`   `// Call the function` `// NumberOfSquares` `echo` `(NumberOfSquares(``\$m``, ``\$n``));`   `// This code is contributed ` `// by akt_mit` `?>`

Javascript

 ``

Output:

`924`

Time complexity: O(log(max(m,n))

Auxiliary Space: O(1)

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