ACSL '09 Practice P3 - Zeroes - Olympiads Online Judge

ACSL '09 Practice P3 - Zeroes

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Points: 10

Time limit: 1.0s

Memory limit: 16M

Problem type

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ALGOL 68, Assembly, Brain****, C, C++, COBOL, Forth, Fortran, Java, Lua, Text, Turing

ACSL Practice 2009

The factorial of a positive integer $n$ ~n~, written as $n!$ ~n!~, is the product of the first $n$ ~n~ positive integers. That is,

$\displaystyle n! = 1 \times 2 \times \dots \times n$

Given a positive integer $n$ ~n~, find the number of zeros in the decimal representation of $n!$ ~n!~. Of course, leading zeros should not be counted. (Note that decimal representation means base ten representation.)

Example 1. There are $7$ ~7~ zeros in the decimal representation of $20!$ ~20!~.

$\displaystyle 20! = 1 \times 2 \times \dots \times 20 = 2432902008176640000$

Example 2. There are $2$ ~2~ zeros in the decimal representation of $7!$ ~7!~.

$\displaystyle 7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 = 5040$

Example 3. There is no zero in the decimal representation of $4!$ ~4!~.

$\displaystyle 4! = 1 \times 2 \times 3 \times 4 = 24$

Input Specification

The input contains a single positive integer $n \le 100$ ~n \le 100~.

Output Specification

The number of zeros in the decimal representation of $n!$ ~n!~.

Sample Input 1

Sample Output 1

Sample Input 2

Sample Output 2

Sample Input 3

Sample Output 3

Comments

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maxcruickshanks commented on Jan. 15, 2022, 10:14 p.m.

Since Java's BigInteger class is unintended and defeats the point of this problem, it has been disabled, and all Java submissions were rejudged.