# First digit in factorial of a number

Given a positive integer n, find the first digit in its factorial.

**Examples :**

Input : n = 5 Output : 1 Factorial of 5 is 120 and first digit is 1. Input : 1000 Output : 4

A **simple solution** is to compute factorial of number, then find first digit in it.

The above solution causes **overflow** soon. A better solution is to use the fact that factorial contains trailing 0s and removing trailing 0s does not change first digit. For example, first digit of x * y is same as x * y * 100 for x > 0 and y > 0.

## C++

`// A C++ program for finding the First digit` `// of the large factorial number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `firstDigit(` `int` `n)` `{` ` ` `long` `long` `int` `fact = 1;` ` ` `for` `(` `int` `i = 2; i <= n; i++) {` ` ` `fact = fact * i;` ` ` `// Removing trailing 0s as this` ` ` `// does not change first digit.` ` ` `while` `(fact % 10 == 0)` ` ` `fact = fact / 10; ` ` ` `}` ` ` `// loop for divide the fact until it` ` ` `// become the single digit and return` ` ` `// the fact` ` ` `while` `(fact >= 10)` ` ` `fact = fact / 10;` ` ` ` ` `return` `fact;` `}` `// derive main` `int` `main()` `{` ` ` `int` `n = 5;` ` ` `cout << firstDigit(n);` ` ` `return` `0;` `}` |

## Java

`// A Java program for finding the First digit` `// of the large factorial number` `class` `GFG{` `static` `int` `firstDigit(` `int` `n)` `{` ` ` `int` `fact = ` `1` `;` ` ` `for` `(` `int` `i = ` `2` `; i <= n; i++) {` ` ` `fact = fact * i;` ` ` `// Removing trailing 0s as this` ` ` `// does not change first digit.` ` ` `while` `(fact % ` `10` `== ` `0` `)` ` ` `fact = fact / ` `10` `; ` ` ` `}` ` ` `// loop for divide the fact until it` ` ` `// become the single digit and return` ` ` `// the fact` ` ` `while` `(fact >= ` `10` `)` ` ` `fact = fact / ` `10` `;` ` ` ` ` `return` `fact;` `}` `// derive main` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `5` `;` ` ` `System.out.println(firstDigit(n));` `}` `}` `//This code is contributed by Smitha Dinesh Semwal` |

## Python3

`# Python3 program for finding` `# the First digit of the` `# large factorial number` `import` `math` `def` `firstDigit(n) :` ` ` `fact ` `=` `1` ` ` `for` `i ` `in` `range` `(` `2` `, n ` `+` `1` `) :` ` ` `fact ` `=` `fact ` `*` `i` ` ` `# Removing trailing 0s` ` ` `# as this does not` ` ` `# change first digit.` ` ` `while` `(fact ` `%` `10` `=` `=` `0` `) :` ` ` `fact ` `=` `int` `(fact ` `/` `10` `)` ` ` `# loop for divide the fact` ` ` `# until it become the single` ` ` `# digit and return the fact` ` ` `while` `(fact >` `=` `10` `) :` ` ` `fact ` `=` `int` `(fact ` `/` `10` `)` ` ` ` ` `return` `math.floor(fact)` `# Driver Code` `n ` `=` `5` `print` `(firstDigit(n))` `# This code is contributed by` `# Manish Shaw(manishshaw1)` |

## C#

`// A C# program for finding the First digit` `// of the large factorial number` `using` `System;` `class` `GFG {` ` ` ` ` `static` `int` `firstDigit(` `int` `n)` ` ` `{` ` ` `int` `fact = 1;` ` ` ` ` `for` `(` `int` `i = 2; i <= n; i++)` ` ` `{` ` ` `fact = fact * i;` ` ` ` ` `// Removing trailing 0s as this` ` ` `// does not change first digit.` ` ` `while` `(fact % 10 == 0)` ` ` `fact = fact / 10; ` ` ` `}` ` ` ` ` `// loop for divide the fact until` ` ` `// it become the single digit and` ` ` `// return the fact` ` ` `while` `(fact >= 10)` ` ` `fact = fact / 10;` ` ` ` ` `return` `fact;` ` ` `}` ` ` ` ` `// driver function` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 5;` ` ` ` ` `Console.Write(firstDigit(n));` ` ` `}` `}` `// This code is contributed by parashar.` |

## PHP

`<?php` `// PHP program for finding` `// the First digit of the` `// large factorial number` `function` `firstDigit(` `$n` `)` `{` ` ` `$fact` `= 1;` ` ` `for` `(` `$i` `= 2; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `{` ` ` `$fact` `= ` `$fact` `* ` `$i` `;` ` ` `// Removing trailing 0s as this` ` ` `// does not change first digit.` ` ` `while` `(` `$fact` `% 10 == 0)` ` ` `$fact` `= ` `$fact` `/ 10;` ` ` `}` ` ` `// loop for divide the fact` ` ` `// until it become the single` ` ` `// digit and return the fact` ` ` `while` `(` `$fact` `>= 10)` ` ` `$fact` `= ` `$fact` `/ 10;` ` ` ` ` `return` `floor` `(` `$fact` `);` `}` `// Driver Code` `$n` `= 5;` `echo` `firstDigit(` `$n` `);` `// This code is contributed by aj_36.` `?>` |

## Javascript

`<script>` `// JavaScript program for finding the` `// First digit of the large factorial number` `function` `firstDigit(n)` `{` ` ` `let fact = 1;` ` ` ` ` `for` `(let i = 2; i <= n; i++)` ` ` `{` ` ` `fact = fact * i;` ` ` ` ` `// Removing trailing 0s as this` ` ` `// does not change first digit.` ` ` `while` `(fact % 10 == 0)` ` ` `fact = fact / 10; ` ` ` `}` ` ` ` ` `// Loop for divide the fact until it` ` ` `// become the single digit and return` ` ` `// the fact` ` ` `while` `(fact >= 10)` ` ` `fact = fact / 10;` ` ` ` ` `return` `(Math.round(fact));` `}` `// Driver code` `let n = 5;` `document.write(firstDigit(n));` `// This code is contributed by splevel62` `</script>` |

**Output :**

1

The above code also fails for slightly higher values. The best idea seems to be to find factorial of large number and then find first digit.