# Efficiently check whether n is a multiple of 4 or not

Given a number **n**. The problem is to efficiently check whether **n** is a multiple of 4 or not without using arithmetic operators. **Examples:**

Input : 16 Output : Yes Input : 14 Output : No

**Approach:** A multiple of 4 always has **00** as its last two digits in its binary representation. We have to check whether the last two digits of **n** are unset or not.**How to check whether the last two bits are unset or not.**

If n & 3 == 0, then the last two bits are unset, else either both or one of them are set.

## C++

`// C++ implementation to efficiently check whether n` `// is a multiple of 4 or not` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function to check whether 'n' is` `// a multiple of 4 or not` `string isAMultipleOf4(` `int` `n)` `{` ` ` ` ` `// if true, then 'n' is a multiple of 4` ` ` `if` `((n & 3) == 0)` ` ` `return` `"Yes"` `;` ` ` `// else 'n' is not a multiple of 4` ` ` `return` `"No"` `;` `}` `// Driver program to test above` `int` `main()` `{` ` ` `int` `n = 16;` ` ` `cout << isAMultipleOf4(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to efficiently check` `// whether n is a multiple of 4 or not` `class` `GFG {` ` ` `// method to check whether 'n' is` ` ` `// a multiple of 4 or not` ` ` `static` `boolean` `isAMultipleOf4(` `int` `n)` ` ` `{` ` ` `// if true, then 'n' is a multiple of 4` ` ` `if` `((n & ` `3` `) == ` `0` `)` ` ` `return` `true` `;` ` ` `// else 'n' is not a multiple of 4` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver method` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `16` `;` ` ` `System.out.println(isAMultipleOf4(n) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` |

## Python 3

`# Python 3 implementation to` `# efficiently check whether n` `# is a multiple of 4 or not` `# function to check whether 'n'` `# is a multiple of 4 or not` `def` `isAMultipleOf4(n):` ` ` `# if true, then 'n' is` ` ` `# a multiple of 4` ` ` `if` `((n & ` `3` `) ` `=` `=` `0` `):` ` ` `return` `"Yes"` ` ` `# else 'n' is not a` ` ` `# multiple of 4` ` ` `return` `"No"` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `n ` `=` `16` ` ` `print` `(isAMultipleOf4(n))` `# This code is contributed` `# by ChitraNayal` |

## C#

`// C# implementation to efficiently check` `// whether n is a multiple of 4 or not` `using` `System;` `class` `GFG {` ` ` ` ` `// method to check whether 'n' is` ` ` `// a multiple of 4 or not` ` ` `static` `bool` `isAMultipleOf4(` `int` `n)` ` ` `{` ` ` `// if true, then 'n' is a multiple of 4` ` ` `if` `((n & 3) == 0)` ` ` `return` `true` `;` ` ` `// else 'n' is not a multiple of 4` ` ` `return` `false` `;` ` ` `}` ` ` `// Driver method` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 16;` ` ` `Console.WriteLine(isAMultipleOf4(n) ? ` `"Yes"` `: ` `"No"` `);` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP implementation to` `// efficiently check whether n` `// is a multiple of 4 or not` `// function to check whether 'n' is` `// a multiple of 4 or not` `function` `isAMultipleOf4(` `$n` `)` `{` ` ` ` ` `// if true, then 'n'` ` ` `// is a multiple of 4` ` ` `if` `((` `$n` `& 3) == 0)` ` ` `return` `"Yes"` `;` ` ` `// else 'n' is not` ` ` `// a multiple of 4` ` ` `return` `"No"` `;` `}` ` ` `// Driver Code` ` ` `$n` `= 16;` ` ` `echo` `isAMultipleOf4(` `$n` `);` ` ` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript implementation to efficiently check` `// whether n is a multiple of 4 or not` ` ` ` ` `// method to check whether 'n' is` ` ` `// a multiple of 4 or not` ` ` `function` `isAMultipleOf4(n)` ` ` `{` ` ` `// if true, then 'n' is a multiple of 4` ` ` `if` `((n & 3) == 0)` ` ` `return` `true` `;` ` ` ` ` `// else 'n' is not a multiple of 4` ` ` `return` `false` `;` ` ` `}` ` ` ` ` `// Driver method` ` ` `let n = 16;` ` ` `document.write(isAMultipleOf4(n) ? ` `"Yes"` `: ` `"No"` `);` ` ` ` ` `//This code is contributed by rag2127` ` ` `</script>` |

Output:

Yes

**Time Complexity : **O(1)

**Auxiliary Space: **O(1)

**Can we generalize above solution?**

Similarly we can check for other powers of 2. For example, a number n would be multiple of 8 if n & 7 is 0. In general we can say.

// x must be a power of 2 for below // logic to work if (n & (x -1) == 0) n is a multiple of x Else n is NOT a multiple of x

https://youtu.be/ke

-Mai2m6Cg

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