Self Dividing Numbers

Self Dividing Numbers - Problem

Math Easy

A self-dividing number is a number that is divisible by every digit it contains.

For example, 128 is a self-dividing number because:

128 % 1 == 0
128 % 2 == 0
128 % 8 == 0

A self-dividing number is not allowed to contain the digit zero.

Given two integers left and right, return a list of all the self-dividing numbers in the range [left, right] (both inclusive).

Input & Output

Example 1 — Basic Range

$ Input: left = 1, right = 22

› Output: [1,2,3,4,5,6,7,8,9,11,12,15,22]

💡 Note: Numbers like 10, 20 contain zero (invalid). 13: 13%3=1≠0 (invalid). 22: 22%2=0 ✓ (valid)

Example 2 — Three-Digit Numbers

$ Input: left = 47, right = 85

› Output: [48,55,66,77]

💡 Note: 48: 48%4=0, 48%8=0 ✓. 55: 55%5=0 ✓. 66: 66%6=0 ✓. 77: 77%7=0 ✓

Example 3 — Single Number Range

$ Input: left = 128, right = 128

› Output: [128]

💡 Note: 128: 128%1=0, 128%2=0, 128%8=0, all digits divide evenly

Constraints

1 ≤ left ≤ right ≤ 10⁴

Visualization

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Asked in

a Amazon 15 G Google 12 M Microsoft 8

The key insight is that a self-dividing number cannot contain zero (division by zero is undefined) and must be divisible by each of its digits. The optimal approach extracts digits mathematically using modulo operations. Time: O(n × d), Space: O(1).

Common Approaches

✓ Brute Force with String Conversion

⏱️ Time: O(n × d) Space: O(1)

For each number in the range, convert it to a string to easily access each digit, then check if the original number is divisible by each digit. Skip numbers containing zero.

Mathematical Digit Extraction

⏱️ Time: O(n × d) Space: O(1)

Use mathematical operations to extract each digit from the number. Extract digits using modulo 10 and integer division, avoiding string conversion overhead.

Brute Force with String Conversion — Algorithm Steps

Step 1: Iterate through each number from left to right
Step 2: Convert number to string to extract individual digits
Step 3: Check if number is divisible by each digit (skip if contains 0)
Step 4: Add valid self-dividing numbers to result list

Visualization

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Step-by-Step Walkthrough

Range Iteration

Check each number from left to right

String Conversion

Convert number to string to access digits

Divisibility Check

Verify number is divisible by each digit

Code -

solution.c — C

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

void solution(int left, int right, int* result, int* size) {
    *size = 0;
    for (int num = left; num <= right; num++) {
        char numStr[20];
        sprintf(numStr, "%d", num);
        int isSelfDividing = 1;
        
        for (int i = 0; numStr[i]; i++) {
            int digit = numStr[i] - '0';
            if (digit == 0 || num % digit != 0) {
                isSelfDividing = 0;
                break;
            }
        }
        
        if (isSelfDividing) {
            result[(*size)++] = num;
        }
    }
}

int main() {
    int left, right;
    scanf("%d %d", &left, &right);
    
    int result[10000];
    int size;
    solution(left, right, result, &size);
    
    printf("[");
    for (int i = 0; i < size; i++) {
        printf("%d", result[i]);
        if (i < size - 1) printf(",");
    }
    printf("]\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × d)

n numbers in range, d average digits per number

✓ Linear Growth

Space Complexity

O(1)

Only using variables, output list not counted

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force with String Conversion — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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