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; } |
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 = 100printFactorialNums(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. ?> |
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.
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