# 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

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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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