# Minimum squares to evenly cut a rectangle

Given a rectangular sheet of length l and width w. we need to divide this sheet in the square sheets such that the number of square sheets should be as minimum as possible.

Examples:

Input :l= 4 w=6
Output :6
We can form squares with side of 1 unit, But the number of squares will be 24, this is not minimum. If we make square with side of 2, then we have 6 squares. and this is our required answer.
And also we can’t make square with side 3, if we select 3 as square side, then whole sheet can’t be converted into suares of equal length. Input :l=3 w=5
Output :15

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

Optimal length of side of a square is equal to GCD of two numbers

## C++

 `// CPP program to find minimum number of ` `// squares to make a given rectangle. ` `#include ` `using` `namespace` `std; ` ` `  `int` `countRectangles(``int` `l, ``int` `w) ` `{ ` `    ``// if we take gcd(l, w), this ` `    ``// will be largest possible ` `    ``// side for suare, hence minimum ` `    ``// number of square. ` `    ``int` `squareSide = __gcd(l, w); ` ` `  `    ``// Number of squares. ` `    ``return` `(l * w) / (squareSide * squareSide); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `l = 4, w = 6; ` `    ``cout << countRectangles(l, w) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java program to find minimum number of ` `// squares to make a given rectangle. ` ` `  `class` `GFG{ ` `static` `int` `__gcd(``int` `a, ``int` `b) { ` `   ``if` `(b==``0``) ``return` `a; ` `   ``return` `__gcd(b,a%b); ` `} ` `static` `int` `countRectangles(``int` `l, ``int` `w) ` `{ ` `    ``// if we take gcd(l, w), this ` `    ``// will be largest possible ` `    ``// side for suare, hence minimum ` `    ``// number of square. ` `    ``int` `squareSide = __gcd(l, w); ` ` `  `    ``// Number of squares. ` `    ``return` `(l * w) / (squareSide * squareSide); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `l = ``4``, w = ``6``; ` `    ``System.out.println(countRectangles(l, w)); ` `} ` `} ` `// This code is contributed by mits `

## Python3

 `# Python3 code to find minimum number of ` `# squares to make a given rectangle. ` ` `  `import` `math  ` ` `  `def` `countRectangles(l, w): ` ` `  `    ``# if we take gcd(l, w), this ` `    ``# will be largest possible ` `    ``# side for suare, hence minimum ` `    ``# number of square. ` `    ``squareSide ``=` `math.gcd(l,w) ` `     `  `    ``# Number of squares. ` `    ``return` `(l``*``w)``/``(squareSide``*``squareSide) ` ` `  `# Driver Code ` `         `  `if` `__name__ ``=``=` `'__main__'``: ` `    ``l ``=` `4` `    ``w ``=` `6` `    ``ans ``=` `countRectangles(l, w) ` `    ``print` `(``int``(ans)) ` ` `  `# this code is contributed by ` `# SURENDRA_GANGWAR `

## C#

 `// C# program to find minimum number of ` `// squares to make a given rectangle. ` ` `  `class` `GFG{ ` `static` `int` `__gcd(``int` `a, ``int` `b) { ` `if` `(b==0) ``return` `a; ` `return` `__gcd(b,a%b); ` `} ` `static` `int` `countRectangles(``int` `l, ``int` `w) ` `{ ` `    ``// if we take gcd(l, w), this ` `    ``// will be largest possible ` `    ``// side for suare, hence minimum ` `    ``// number of square. ` `    ``int` `squareSide = __gcd(l, w); ` ` `  `    ``// Number of squares. ` `    ``return` `(l * w) / (squareSide * squareSide); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `l = 4, w = 6; ` `    ``System.Console.WriteLine(countRectangles(l, w)); ` `} ` `} ` `// This code is contributed by mits `

## PHP

 ` `

Output:

```6
```

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