Count the Digits That Divide a Number

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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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

✓ Extract Digits Using Modulo

⏱️ Time: O(log n) Space: O(1)

Use mathematical operations to extract each digit from right to left, then check if each non-zero digit divides the original number evenly.

String Conversion Approach

⏱️ Time: O(log n) Space: O(log n)

Convert the number to a string to easily access each digit, then check if each non-zero digit divides the original number evenly.

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

28.0K Views

Medium Frequency

~10 min Avg. Time

892 Likes

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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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