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.

An integer val divides nums if nums % val == 0.

Note: We cannot divide by zero, so digits equal to 0 should be ignored.

Input & Output

Example 1 — Basic Case

$ Input: num = 121

› Output: 2

💡 Note: 121 has digits 1, 2, 1. Digit 1 divides 121 (121/1 = 121), digit 2 does not divide 121 (121/2 = 60.5), digit 1 divides 121. So 2 digits divide 121.

Example 2 — All Digits Divide

$ Input: num = 1248

› Output: 4

💡 Note: 1248 has digits 1, 2, 4, 8. All digits divide 1248 evenly: 1248/1=1248, 1248/2=624, 1248/4=312, 1248/8=156. So all 4 digits divide the number.

Example 3 — Zero Digit

$ Input: num = 1012

› Output: 3

💡 Note: 1012 has digits 1, 0, 1, 2. We ignore 0 (can't divide by zero). Digits 1, 1, and 2 all divide 1012 evenly, so count is 3.

Constraints

1 ≤ num ≤ 10⁹
num does not contain 0 as a digit in most test cases

Visualization

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Understanding the Visualization

Input

Number 232 with digits 2, 3, 2

Process

Check each digit: 232%2=0✓, 232%3≠0✗, 232%2=0✓

Output

Count of 2 digits that divide evenly

Key Takeaway

🎯 Key Insight: Extract each digit and count how many divide the original number with zero remainder

Asked in

A Amazon 25 M Microsoft 15

The key insight is to extract each digit and test divisibility while ignoring zeros. Best approach converts to string for easy digit access. Time: O(log n), Space: O(log n) for string approach or O(1) for mathematical approach.

Common Approaches

Approach	Time	Space	Notes
✓ Extract Digits Using Modulo	O(log n)	O(1)	Extract digits using modulo and division operations
String Conversion Approach	O(log n)	O(log n)	Convert number to string and iterate through each character

Extract Digits Using Modulo — Algorithm Steps

Step 1: Extract rightmost digit using num % 10
Step 2: Check if digit != 0 and num % digit == 0
Step 3: Remove rightmost digit using num / 10
Step 4: Repeat until no digits left

Visualization

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Step-by-Step Walkthrough

Extract Digit

Use num % 10 to get rightmost digit

Check Divisibility

Test if original % digit == 0

Remove Digit

Use num / 10 to remove processed digit

Code -

solution.c — C

#include <stdio.h>

int solution(int num) {
    int original = num;
    int count = 0;
    
    while (num > 0) {
        int digit = num % 10;
        if (digit != 0 && original % digit == 0) {
            count++;
        }
        num = num / 10;
    }
    
    return count;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(log n)

We process each digit once, and there are log₁₀(n) digits in number n

⚡ Linearithmic

Space Complexity

O(1)

Only using a few variables to track count and temporary values

✓ Linear Space

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Medium Frequency

~10 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Extract Digits Using Modulo — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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