Factorial Trailing Zeroes

Problem Statement

Given an integer n, return the number of trailing zeroes in n!.

You need to solve this problem efficiently.

What to notice first

• Key insight 1 for Factorial Trailing Zeroes
• Key insight 2 for solving this problem
• Key insight 3 specific to the approach

Examples

Input	Output	Explanation
Example 1	Result 1	Explanation for example 1
Example 2	Result 2	Explanation for example 2

Constraints

• Constraint 1 for Factorial Trailing Zeroes
• Constraint 2
• Constraint 3

Real-World Applications

Where this pattern appears

• Database indexing and query optimization
• Buffer management in system memory
• Time-series data analysis and sliding windows
• Image pixel manipulation and batch processing

Complexity Comparison

Approach	Time	Space	Best When
Count Fives	O(n)	O(1)	When applicable
Iterative	O(n)	O(1)	When applicable
Formula	O(n)	O(1)	When applicable

Approach 1: Count Fives

★ Recommended

This approach provides an efficient solution for factorial trailing zeroes.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

factorial_trailing_zeroes_count_fives.py

def factorial_trailing_zeroes_count_fives(n: int) -> int:
    """Count trailing zeroes in n! by counting factors of 5."""
    count = 0
    power_of_5 = 5
    while power_of_5 <= n:
        count += n // power_of_5
        power_of_5 *= 5
    return count

# Test cases
print(factorial_trailing_zeroes_count_fives(5))  # 1
print(factorial_trailing_zeroes_count_fives(25))  # 6

C++

factorial_trailing_zeroes_count_fives.cpp

using namespace std;

int factorialTrailingZeroesCountFives(int n) {
    int count = 0;
    long long powerOf5 = 5;
    while (powerOf5 <= n) {
        count += n / powerOf5;
        powerOf5 *= 5;
    }
    return count;
}

int main() {
    cout << factorialTrailingZeroesCountFives(5) << endl;  // 1
    cout << factorialTrailingZeroesCountFives(25) << endl;  // 6
    return 0;
}

Java

factorial_trailing_zeroes_count_fives.java

public class FactorialTrailingZeroesCountFives {
    public static int factorialTrailingZeroesCountFives(int n) {
        int count = 0;
        long powerOf5 = 5;
        while (powerOf5 <= n) {
            count += n / powerOf5;
            powerOf5 *= 5;
        }
        return count;
    }

    public static void main(String[] args) {
        System.out.println(factorialTrailingZeroesCountFives(5));  // 1
        System.out.println(factorialTrailingZeroesCountFives(25));  // 6
    }
}

JavaScript

factorial_trailing_zeroes_count_fives.js

function factorialTrailingZeroesCountFives(n) {
    let count = 0;
    let powerOf5 = 5;
    while (powerOf5 <= n) {
        count += Math.floor(n / powerOf5);
        powerOf5 *= 5;
    }
    return count;
}

console.log(factorialTrailingZeroesCountFives(5));  // 1
console.log(factorialTrailingZeroesCountFives(25));  // 6

Rust

factorial_trailing_zeroes_count_fives.rs

fn factorial_trailing_zeroes_count_fives(n: i32) -> i32 {
    let mut count = 0;
    let mut power_of_5 = 5i64;
    while power_of_5 <= n as i64 {
        count += n as i64 / power_of_5;
        power_of_5 *= 5;
    }
    count as i32
}

fn main() {
    println!("{}", factorial_trailing_zeroes_count_fives(5));  // 1
    println!("{}", factorial_trailing_zeroes_count_fives(25));  // 6
}

Go

factorial_trailing_zeroes_count_fives.go

package main

import "fmt"

func factorialTrailingZeroesCountFives(n int) int {
  count := 0
  powerOf5 := 5
  for powerOf5 <= n {
    count += n / powerOf5
    powerOf5 *= 5
  }
  return count
}

func main() {
  fmt.Println(factorialTrailingZeroesCountFives(5))  // 1
  fmt.Println(factorialTrailingZeroesCountFives(25))  // 6
}

Approach 2: Iterative

🎯 Interview Favourite

This approach provides an efficient solution for factorial trailing zeroes.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

factorial_trailing_zeroes_iterative.py

# Python Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

C++

factorial_trailing_zeroes_iterative.cpp

# C++ Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

Java

factorial_trailing_zeroes_iterative.java

# Java Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

JavaScript

factorial_trailing_zeroes_iterative.js

# JavaScript Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

Rust

factorial_trailing_zeroes_iterative.rs

# Rust Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

Go

factorial_trailing_zeroes_iterative.go

# Golang Solution
# Problem: factorial-trailing-zeroes
# Approach: iterative

# Implementation placeholder for factorial_trailing_zeroes_iterative
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_iterative():
    pass

if __name__ == "__main__":
    pass

Approach 3: Formula

✓ Simple

This approach provides an efficient solution for factorial trailing zeroes.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

factorial_trailing_zeroes_formula.py

# Python Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

C++

factorial_trailing_zeroes_formula.cpp

# C++ Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

Java

factorial_trailing_zeroes_formula.java

# Java Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

JavaScript

factorial_trailing_zeroes_formula.js

# JavaScript Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

Rust

factorial_trailing_zeroes_formula.rs

# Rust Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

Go

factorial_trailing_zeroes_formula.go

# Golang Solution
# Problem: factorial-trailing-zeroes
# Approach: formula

# Implementation placeholder for factorial_trailing_zeroes_formula
# This file is auto-generated and should contain the solution code.

def factorial_trailing_zeroes_formula():
    pass

if __name__ == "__main__":
    pass

Related Problems

• Two Sum ↗ Easy #1
• Palindrome Number ↗ Easy #9

Interview Tips

Key trade-offs to discuss

• Time vs. space trade-offs between approaches
• Handling edge cases (empty inputs, single elements, duplicates)
• Optimization opportunities and when they matter
• Follow-up variations and constraint changes

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