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

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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,

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

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 $20!$ $20!$ .

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

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

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

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

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

Input Specification

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

Output Specification

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

Sample Input 1

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Sample Output 1

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Sample Input 2

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Sample Output 2

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Sample Input 3

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Sample Output 3

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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.