# Find all factorial numbers less than or equal to n

A number N is called a factorial number if it is the factorial of a positive integer. For example, the first few factorial numbers are

1, 2, 6, 24, 120, …

Given a number n, print all factorial numbers smaller than or equal to n. **Examples : **

Input : n = 100 Output : 1 2 6 24 Input : n = 1500 Output : 1 2 6 24 120 720

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A **simple solution **is to generate all factorials one by one until the generated factorial is greater than n.

An **efficient solution** is to find next factorial using previous factorial.

## C++

`// CPP program to find all factorial numbers` `// smaller than or equal to n.` `#include <iostream>` `using` `namespace` `std;` `void` `printFactorialNums(` `int` `n)` `{` ` ` `int` `fact = 1;` ` ` `int` `x = 2;` ` ` `while` `(fact <= n) {` ` ` `cout << fact << ` `" "` `;` ` ` `// Compute next factorial` ` ` `// using previous` ` ` `fact = fact * x;` ` ` `x++;` ` ` `}` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 100;` ` ` `printFactorialNums(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find all factorial numbers` `// smaller than or equal to n.` `class` `GFG` `{` ` ` `static` `void` `printFactorialNums(` `int` `n)` ` ` `{` ` ` `int` `fact = ` `1` `;` ` ` `int` `x = ` `2` `;` ` ` `while` `(fact <= n)` ` ` `{` ` ` `System.out.print(fact + ` `" "` `);` ` ` ` ` `// Compute next factorial` ` ` `// using previous` ` ` `fact = fact * x;` ` ` ` ` `x++;` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `100` `;` ` ` `printFactorialNums(n);` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`# Python3 program to find all factorial` `# numbers smaller than or equal to n.` `def` `printFactorialNums( n):` ` ` `fact ` `=` `1` ` ` `x ` `=` `2` ` ` `while` `fact <` `=` `n:` ` ` `print` `(fact, end ` `=` `" "` `)` ` ` ` ` `# Compute next factorial` ` ` `# using previous` ` ` `fact ` `=` `fact ` `*` `x` ` ` ` ` `x ` `+` `=` `1` `# Driver code` `n ` `=` `100` `printFactorialNums(n)` `# This code is contributed by "Abhishek Sharma 44"` |

## C#

`// C# program to find all factorial numbers` `// smaller than or equal to n.` `using` `System;` `class` `GFG` `{` ` ` `static` `void` `printFactorialNums(` `int` `n)` ` ` `{` ` ` `int` `fact = 1;` ` ` `int` `x = 2;` ` ` `while` `(fact <= n)` ` ` `{` ` ` `Console.Write(fact + ` `" "` `);` ` ` ` ` `// Compute next factorial` ` ` `// using previous` ` ` `fact = fact * x;` ` ` ` ` `x++;` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `n = 100;` ` ` `printFactorialNums(n);` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find all` `// factorial numbers smaller` `// than or equal to n.` `function` `printFactorialNums(` `$n` `)` `{` ` ` `$fact` `= 1;` ` ` `$x` `= 2;` ` ` `while` `(` `$fact` `<= ` `$n` `)` ` ` `{` ` ` `echo` `$fact` `, ` `" "` `;` ` ` `// Compute next factorial` ` ` `// using previous` ` ` `$fact` `= ` `$fact` `* ` `$x` `;` ` ` `$x` `++;` ` ` `}` `}` ` ` `// Driver code` ` ` `$n` `= 100;` ` ` `echo` `printFactorialNums(` `$n` `);` `// This code is contributed by ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to find all factorial numbers` `// smaller than or equal to n.` `function` `printFactorialNums(n)` `{` ` ` `let fact = 1;` ` ` `let x = 2;` ` ` `while` `(fact <= n) {` ` ` `document.write(fact + ` `" "` `);` ` ` `// Compute next factorial` ` ` `// using previous` ` ` `fact = fact * x;` ` ` `x++;` ` ` `}` `}` `// Driver code` ` ` `let n = 100;` ` ` `printFactorialNums(n);` `// This code is contributed by Mayank Tyagi` ` ` `</script>` |

Output:

1 2 6 24

Time Complexity : O(n)

If there are multiple queries, then we can cache all previously computed factorial numbers to avoid re-computations.

This article is contributed by **Shubham Sagar**. 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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