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.
// 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;
}
// 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 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)
// 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 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.
?>
<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
Time Complexity: O(n * log10(n)), where log10(n) time is to remove trailing zeroes and it is running n times
Auxiliary Space: O(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.
