Trailing Zero

Number Theory Level 3

We know,

N! = 1 X 2 X 3 X ........ X (N-1) X N .

Now , 5! = 1 X 2 X 3 X 4 X 5 = 120 .

So 5! contains one trailing 0 .

Now you to tell me , how many trailing zero contains 1000000!

The answer is 249998.

1 solution

Parveen Soni
Oct 29, 2014

keep on dividing 1000000 to 5^1 and 5^2 and 5^3 and so on till you get value less than one.
now add values of all division and you will get answer

For Programmer my java program is --------------------------------------->>>>>> public class program {
public static void main(String[] args)
{ System.out.println(countTrailingZerosOfFactorial(1000000)); }
private static final int countTrailingZerosOfFactorial(final int n) {
int count = 0;
for (int factor = 5; factor <= n; factor += 5) count += countFives(factor); return count; }
private static final int countFives(int factor) {
if (!divides(5, factor))
return 0;
return 1 + countFives(factor / 5); }
private static final boolean divides(final int d, final int n) { return n % d == 0; }
}

Parveen Soni - 6 years, 7 months ago

Trailing Zero

The answer is 249998.

1 solution

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