Count the Digits That Divide a Number - Practice Coding Problems

Count the Digits That Divide a Number - Problem

Math Easy

Given an integer num, return the number of digits in num that divide num evenly.

A digit val divides num if num % val == 0.

Note: We only consider non-zero digits, as division by zero is undefined.

Example: For num = 1248, the digits are 1, 2, 4, 8. We check: 1248 % 1 = 0 ✓, 1248 % 2 = 0 ✓, 1248 % 4 = 0 ✓, 1248 % 8 = 0 ✓. All 4 digits divide the number, so we return 4.

This problem tests your understanding of digit extraction and modular arithmetic.

Input & Output

example_1.py — Basic Case

$ Input: num = 7

› Output: 1

💡 Note: The only digit is 7, and 7 % 7 = 0, so 7 divides 7. Return 1.

example_2.py — Multiple Digits

$ Input: num = 1248

› Output: 4

💡 Note: Digits are 1, 2, 4, 8. Check: 1248 % 1 = 0, 1248 % 2 = 0, 1248 % 4 = 0, 1248 % 8 = 0. All 4 digits divide 1248.

example_3.py — With Non-Divisible Digits

$ Input: num = 121

› Output: 2

💡 Note: Digits are 1, 2, 1. Check: 121 % 1 = 0 ✓, 121 % 2 = 1 ✗, 121 % 1 = 0 ✓. Only 2 digits divide 121.

Constraints

1 ≤ num ≤ 10⁹
num does not contain 0 as a digit

Visualization

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Understanding the Visualization

Component Extraction

Extract each digit component from the product using mathematical operations

Quality Test

Test if the component (digit) is compatible with the product (original number)

Count Valid Components

Keep track of how many components pass the quality test

Final Report

Return the total count of compatible components

Key Takeaway

🎯 Key Insight: Mathematical digit extraction using modulo and division is more efficient than string conversion, providing O(1) space complexity while maintaining O(d) time complexity.

Asked in

G Google 15 a Amazon 12 f Meta 8 ⊞ Microsoft 6

The optimal solution uses mathematical digit extraction with num % 10 to get digits and num // 10 to remove them. This avoids string conversion overhead and runs in O(d) time and O(1) space, where d is the number of digits. The key insight is that we can process digits mathematically without converting to strings.

Common Approaches

Approach	Time	Space	Notes
✓ String Conversion Approach	O(d)	O(d)	Convert number to string, iterate through each character digit
Mathematical Digit Extraction (Optimal)	O(d)	O(1)	Extract digits using modulo and division operations without string conversion

String Conversion Approach — Algorithm Steps

Convert the number to a string
Initialize a counter to 0
Iterate through each character in the string
Convert character to integer digit
Skip if digit is 0 (division by zero)
Check if original number is divisible by the digit
Increment counter if divisible
Return the counter

Visualization

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Step-by-Step Walkthrough

Convert to String

Convert 1248 to string '1248'

Extract Digits

Iterate through '1', '2', '4', '8'

Check Divisibility

For each digit, check if 1248 % digit == 0

Count Valid Digits

Count digits that divide evenly

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int countDigits(int num) {
    int count = 0;
    char numStr[12];
    sprintf(numStr, "%d", num);
    
    for (int i = 0; i < strlen(numStr); i++) {
        int digit = numStr[i] - '0';
        if (digit != 0 && num % digit == 0) {
            count++;
        }
    }
    
    return count;
}

int main() {
    int num;
    scanf("%d", &num);
    printf("%d\n", countDigits(num));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(d)

Where d is the number of digits. We iterate through each digit once.

✓ Linear Growth

Space Complexity

O(d)

We create a string representation of the number which takes O(d) space.

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

String Conversion Approach — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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