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

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; ` `} ` |

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## 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. ` |

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## 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" ` |

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## 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. ` |

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## 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. ` `?> ` |

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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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