# Find minimum number to be divided to make a number a perfect square

Given a positive integer **n**. Find the minimum number which divide n to make it a perfect square.**Examples:**

Input : n = 50 Output : 2 By Dividing n by 2, we get which is a perfect square. Input : n = 6 Output : 6 By Dividing n by 6, we get which is a perfect square. Input : n = 36 Output : 1

A number is perfect square if all prime factors appear even number of times. The idea is to find the prime factor of n and find each prime factor power. Now, find and multiply all the prime factor whose power is odd. The resultant of the multiplication is the answer.

## C++

`// C++ program to find minimum number which divide n` `// to make it a perfect square.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Return the minimum number to be divided to make` `// n a perfect square.` `int` `findMinNumber(` `int` `n)` `{` ` ` `int` `count = 0, ans = 1;` ` ` `// Since 2 is only even prime, compute its` ` ` `// power seprately.` ` ` `while` `(n%2 == 0)` ` ` `{` ` ` `count++;` ` ` `n /= 2;` ` ` `}` ` ` `// If count is odd, it must be removed by dividing` ` ` `// n by prime number.` ` ` `if` `(count%2)` ` ` `ans *= 2;` ` ` `for` `(` `int` `i = 3; i <= ` `sqrt` `(n); i += 2)` ` ` `{` ` ` `count = 0;` ` ` `while` `(n%i == 0)` ` ` `{` ` ` `count++;` ` ` `n /= i;` ` ` `}` ` ` `// If count is odd, it must be removed by` ` ` `// dividing n by prime number.` ` ` `if` `(count%2)` ` ` `ans *= i;` ` ` `}` ` ` `if` `(n > 2)` ` ` `ans *= n;` ` ` `return` `ans;` `}` `// Driven Program` `int` `main()` `{` ` ` `int` `n = 72;` ` ` `cout << findMinNumber(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find minimum number` `// which divide n to make it a perfect square.` `class` `GFG` `{` ` ` `// Return the minimum number to be` ` ` `// divided to make n a perfect square.` ` ` `static` `int` `findMinNumber(` `int` `n)` ` ` `{` ` ` `int` `count = ` `0` `, ans = ` `1` `;` ` ` ` ` `// Since 2 is only even prime,` ` ` `// compute its power seprately.` ` ` `while` `(n % ` `2` `== ` `0` `)` ` ` `{` ` ` `count++;` ` ` `n /= ` `2` `;` ` ` `}` ` ` ` ` `// If count is odd, it must be removed by dividing` ` ` `// n by prime number.` ` ` `if` `(count % ` `2` `== ` `1` `)` ` ` `ans *= ` `2` `;` ` ` ` ` `for` `(` `int` `i = ` `3` `; i <= Math.sqrt(n); i += ` `2` `)` ` ` `{` ` ` `count = ` `0` `;` ` ` `while` `(n % i == ` `0` `)` ` ` `{` ` ` `count++;` ` ` `n /= i;` ` ` `}` ` ` ` ` `// If count is odd, it must be removed by` ` ` `// dividing n by prime number.` ` ` `if` `(count % ` `2` `== ` `1` `)` ` ` `ans *= i;` ` ` `}` ` ` ` ` `if` `(n > ` `2` `)` ` ` `ans *= n;` ` ` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `72` `;` ` ` `System.out.println(findMinNumber(n));` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`# Python program to find` `# minimum number which` `# divide n to make it a` `# perfect square.` `import` `math` `# Return the minimum` `# number to be divided` `# to make n a perfect` `# square.` `def` `findMinNumber(n):` ` ` `count ` `=` `0` ` ` `ans ` `=` `1` ` ` `# Since 2 is only` ` ` `# even prime, compute` ` ` `# its power seprately.` ` ` `while` `n ` `%` `2` `=` `=` `0` `:` ` ` `count ` `+` `=` `1` ` ` `n ` `/` `/` `=` `2` ` ` `# If count is odd,` ` ` `# it must be removed` ` ` `# by dividing n by` ` ` `# prime number.` ` ` `if` `count ` `%` `2` `is` `not` `0` `:` ` ` `ans ` `*` `=` `2` ` ` `for` `i ` `in` `range` `(` `3` `, (` `int` `)(math.sqrt(n)) ` `+` `1` `, ` `2` `):` ` ` `count ` `=` `0` ` ` `while` `n ` `%` `i ` `=` `=` `0` `:` ` ` `count ` `+` `=` `1` ` ` `n ` `/` `/` `=` `i` ` ` `# If count is odd, it` ` ` `# must be removed by` ` ` `# dividing n by prime` ` ` `# number.` ` ` `if` `count ` `%` `2` `is` `not` `0` `:` ` ` `ans ` `*` `=` `i` ` ` `if` `n > ` `2` `:` ` ` `ans ` `*` `=` `n` ` ` `return` `ans` `# Driver Code` `n ` `=` `72` `print` `(findMinNumber(n))` `# This code is contributed` `# by Sanjit_Prasad.` |

## C#

`// C# program to find minimum` `// number which divide n to` `// make it a perfect square.` `using` `System;` `class` `GFG` `{` ` ` ` ` `// Return the minimum number` ` ` `// to be divided to make` ` ` `// n a perfect square.` ` ` `static` `int` `findMinNumber(` `int` `n)` ` ` `{` ` ` `int` `count = 0, ans = 1;` ` ` ` ` `// Since 2 is only even prime,` ` ` `// compute its power seprately.` ` ` `while` `(n % 2 == 0)` ` ` `{` ` ` `count++;` ` ` `n /= 2;` ` ` `}` ` ` ` ` `// If count is odd, it must` ` ` `// be removed by dividing` ` ` `// n by prime number.` ` ` `if` `(count % 2 == 1)` ` ` `ans *= 2;` ` ` ` ` `for` `(` `int` `i = 3; i <= Math.Sqrt(n);` ` ` `i += 2)` ` ` `{` ` ` `count = 0;` ` ` `while` `(n % i == 0)` ` ` `{` ` ` `count++;` ` ` `n /= i;` ` ` `}` ` ` ` ` `// If count is odd, it must` ` ` `// be removed by dividing n` ` ` `// by prime number.` ` ` `if` `(count % 2 == 1)` ` ` `ans *= i;` ` ` `}` ` ` ` ` `if` `(n > 2)` ` ` `ans *= n;` ` ` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `n = 72;` ` ` `Console.WriteLine(findMinNumber(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find minimum` `// number which divide n` `// to make it a perfect square.` `// Return the minimum number` `// to be divided to make` `// n a perfect square.` `function` `findMinNumber(` `$n` `)` `{` ` ` `$count` `= 0;` ` ` `$ans` `= 1;` ` ` `// Since 2 is only` ` ` `// even prime,` ` ` `// compute its` ` ` `// power seprately.` ` ` `while` `(` `$n` `% 2 == 0)` ` ` `{` ` ` `$count` `++;` ` ` `$n` `/= 2;` ` ` `}` ` ` `// If count is odd,` ` ` `// it must be removed` ` ` `// by dividing n by` ` ` `// prime number.` ` ` `if` `(` `$count` `% 2)` ` ` `$ans` `*= 2;` ` ` `for` `(` `$i` `= 3; ` `$i` `<= sqrt(` `$n` `); ` `$i` `+= 2)` ` ` `{` ` ` `$count` `= 0;` ` ` `while` `(` `$n` `% ` `$i` `== 0)` ` ` `{` ` ` `$count` `++;` ` ` `$n` `/= ` `$i` `;` ` ` `}` ` ` `// If count is odd,` ` ` `// it must be removed` ` ` `// by dividing n by` ` ` `// prime number.` ` ` `if` `(` `$count` `% 2)` ` ` `$ans` `*= ` `$i` `;` ` ` `}` ` ` `if` `(` `$n` `> 2)` ` ` `$ans` `*= ` `$n` `;` ` ` `return` `$ans` `;` `}` ` ` `// Driver Code` ` ` `$n` `= 72;` ` ` `echo` `findMinNumber(` `$n` `), ` `"\n"` `;` ` ` `// This code is contributed by ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to find minimum` `// number which divide n` `// to make it a perfect square.` `// Return the minimum number` `// to be divided to make` `// n a perfect square.` `function` `findMinNumber(n)` `{` ` ` `let count = 0;` ` ` `let ans = 1;` ` ` `// Since 2 is only` ` ` `// even prime,` ` ` `// compute its` ` ` `// power seprately.` ` ` `while` `(n % 2 == 0)` ` ` `{` ` ` `count++;` ` ` `n /= 2;` ` ` `}` ` ` `// If count is odd,` ` ` `// it must be removed` ` ` `// by dividing n by` ` ` `// prime number.` ` ` `if` `(count % 2)` ` ` `ans *= 2;` ` ` `for` `(let i = 3; i <= Math.sqrt(n); i += 2)` ` ` `{` ` ` `count = 0;` ` ` `while` `(n % i == 0)` ` ` `{` ` ` `count++;` ` ` `n /= i;` ` ` `}` ` ` `// If count is odd,` ` ` `// it must be removed` ` ` `// by dividing n by` ` ` `// prime number.` ` ` `if` `(count % 2)` ` ` `ans *= i;` ` ` `}` ` ` `if` `(n > 2)` ` ` `ans *= n;` ` ` `return` `ans;` `}` ` ` `// Driver Code` ` ` `let n = 72;` ` ` `document.write(findMinNumber(n) + ` `"\n"` `);` ` ` `// This code is contributed by _saurabh_jaiswal.` `</script>` |

**Output:**

2

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