# 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++

`// 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; ` `} ` |

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## 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"` `); ` ` ` `} ` `} ` |

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## 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 ` |

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## 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. ` |

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## 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. ` `?> ` |

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Output:

Yes

**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) == n) n is a multiple of x Else n is NOT a multiple of x

This article is contributed by **Ayush Jauhri**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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