DSA interview question

Count Digits That Evenly Divide N

Easy · Algorithms · Topics: basic maths, number theory

The problem

A number-puzzle app awards a badge for "self-divisible" numbers, and its scoring rule is: for each digit of N, check whether that digit divides N with no remainder, and count how many do. A zero digit can't divide anything, so it's skipped, and repeated digits count once for each occurrence. The heart of the task is the most important basic-maths technique in DSA: pulling digits out of a number one at a time with % 10 and / 10, while keeping the original number intact so you can still test divisibility against it.

Example: N = 1012 has digits 1, 0, 1, 2. Zero is skipped; 1, 1 and 2 all divide 1012, so the answer is 3.

Function signature

int evenlyDivides(int n);  // count of digits d of n with d != 0 and n % d == 0

Test cases

Input `n`	Output	Explanation
12	2	12 % 1 == 0 and 12 % 2 == 0
1012	3	Digits 1, 1, 2 divide; the 0 is skipped
23	0	23 % 2 == 1 and 23 % 3 == 2
5	1	A single-digit number always divides itself
101	2	Both 1s count; 0 is skipped
111	3	Repeated digits each count
100000	1	Only the leading 1 is a usable digit

(Confirm: 1 ≤ n ≤ 10^9; every occurrence of a digit counts separately; zero digits are ignored.)

How interviewers phrase it

"Count the digits of N that evenly divide N" (GeeksforGeeks "Count Digits").
As a simpler warm-up: "Count the number of digits in N" or "Find the sum of the digits of N".
As a building block before reverse-a-number, palindrome-number and Armstrong-number problems, which use the same digit extraction loop.

Clarifying questions to ask

How should zero digits be treated? (They can't be divisors.)
Do repeated digits count once or once per occurrence?
Can N be negative or zero?
What's the range of N?

Follow-ups to expect

"How do you get the last digit and remove it?"
"Why work on a copy of N?"
"What's the time complexity?"
"How would you just count the digits?"
"What about negative N?"

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