18 Harshad
- Sum
- 9, 18 ÷ 9 = 2
Check Harshad Number in C#
What you’ll learn
- What a Harshad number (Niven number) is: divisible by the sum of its digits.
- How to write
IsHarshadNumberin C# with a simple digit-sum loop and modulo check. - How to list Harshad numbers in a range (1–20) and verify results with a live preview.
Overview
Harshad numbers are a gentle interview warm-up: add the digits, then test divisibility. No recursion, no cycles — just modular arithmetic and a digit loop you will reuse in many other problems.
Two programs
Single check for 18 and a range scan 1–20.
Live preview
Type a positive integer and see digit sum plus the divisibility verdict.
Also called Niven
Same definition — divisibility by digit sum — under two common names.
Prerequisites
Digit extraction with % 10 and / 10, modulo, and while loops.
using System;,staticmethods,boolreturn types, string interpolation.- Know that
a % b == 0meansais evenly divisible byb.
What is a Harshad number?
A Harshad number (also called a Niven number) is a positive integer that is divisible by the sum of its decimal digits.
For 18: digits sum to 1 + 8 = 9, and 18 ÷ 9 = 2 with no remainder — so 18 is Harshad. For 11: digit sum is 2, but 11 is not divisible by 2.
18 18 % 9 = 0
11 11 % 2 ≠ 0
10 sum = 1
Formal rule
Let S(n) be the sum of decimal digits of positive integer n. Then n is Harshad when S(n) > 0 and n mod S(n) = 0.
18S(18) = 9 and 18 mod 9 = 0 → Harshad.
Quick examples
11 Not
- Sum
- 2, 11 ÷ 2 has remainder
Harshad numbers 1–20: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20.
Live preview
Enter a positive integer. The widget computes the digit sum and checks divisibility.
Algorithm
Goal: return whether positive n is Harshad.
Save the original
Store originalNumber = n before you peel digits off n.
Sum the digits
While n > 0: add n % 10 to a running sum, then n /= 10.
Test divisibility
Return originalNumber % sumOfDigits == 0 when sumOfDigits > 0.
📜 Pseudocode
Pseudocode
function isHarshad(n): // n > 0
original ← n
sum ← 0
while n > 0:
sum ← sum + (n mod 10)
n ← floor(n / 10)
return (original mod sum) = 01Single check: is
Single check: is 18 Harshad?
Classic reference solution: compute digit sum, then test originalNumber % sumOfDigits == 0.
c#
using System;
class Program
{
static bool IsHarshadNumber(int number)
{
if (number <= 0)
{
return false;
}
int originalNumber = number;
int sumOfDigits = 0;
while (number > 0)
{
sumOfDigits += number % 10;
number /= 10;
}
return originalNumber % sumOfDigits == 0;
}
static void Main()
{
int number = 18;
if (IsHarshadNumber(number))
{
Console.WriteLine($"{number} is a Harshad number.");
}
else
{
Console.WriteLine($"{number} is not a Harshad number.");
}
}
}Explanation
The loop destroys number while building sumOfDigits, so we keep originalNumber for the final modulo test.
return originalNumber % sumOfDigits == 0;Core test. Harshad means zero remainder when dividing by the digit sum.
2Harshad numbers from
Harshad numbers from 1 to 20
Reuses IsHarshad inside a for loop to print every Harshad number in the range — same output as the reference tutorial.
c#
using System;
class Program
{
static bool IsHarshad(int number)
{
if (number <= 0)
{
return false;
}
int sumOfDigits = 0;
int originalNumber = number;
while (number > 0)
{
sumOfDigits += number % 10;
number /= 10;
}
return originalNumber % sumOfDigits == 0;
}
static void Main()
{
Console.WriteLine("Harshad numbers in the range 1 to 20:");
for (int i = 1; i <= 20; i++)
{
if (IsHarshad(i))
{
Console.Write($"{i} ");
}
}
Console.WriteLine();
}
}Explanation
Numbers 11, 13, 14, etc. fail the divisibility test. Single-digit values always pass because the digit sum equals the number itself.
Beyond the basics
Extract SumOfDigits. Pull digit summing into its own method — you will reuse it in Armstrong, Disarium, and divisor problems.
Console input. Wrap with int.TryParse when reading from Console.ReadLine().
Interview: state the definition, walk through 18, mention 0 and negatives as out-of-scope, then write the digit loop.
❓ FAQ
A positive integer that is divisible by the sum of its decimal digits. It is also called a Niven number.
Yes. Digit sum is 1 + 8 = 9, and 18 ÷ 9 = 2 with no remainder.
No. Digit sum is 1 + 1 = 2, and 11 is not divisible by 2.
Yes for 1–9. Each number n is divisible by n (the only digit).
Yes. Digit sum is 1 + 0 = 1, and every integer is divisible by 1.
Harshad numbers are defined for positive integers. Zero has digit sum 0, which would cause division by zero — reject or handle separately.
Happy numbers repeat sum of squares of digits until reaching 1. Harshad numbers only check one step: divisibility by the digit sum.
🔄 Input / output examples
Change number in Main, or read from the console after validation.
| Input | Digit sum | Verdict |
|---|---|---|
1 | 1 | Harshad |
10 | 1 | Harshad |
12 | 3 | Harshad (12 ÷ 3 = 4) |
18 | 9 | Harshad (18 ÷ 9 = 2) |
11 | 2 | Not Harshad |
13 | 4 | Not Harshad |
Edge cases and pitfalls
The logic is simple, but two corners need explicit handling in production code.
Zero
0
Digit sum is 0 — dividing by zero throws. Return false or reject early.
Negative
n < 0
Outside the usual definition — return false or use Math.Abs only if your spec allows it.
Single digit
1–9
Always Harshad: n % n == 0 when the only digit is n.
Overwrite
Losing the original
If you forget originalNumber, the digit loop leaves number == 0 and the modulo test is wrong.
⏱️ Time and space complexity
| Operation | Time | Extra space |
|---|---|---|
| Single check | O(log n) digits | O(1) |
| Range 1–20 scan | O(20 × log n) | O(1) |
Digit count grows with the number of decimal places — logarithmic in the value of n.
Summary
- Definition: positive
ndivisible by the sum of its decimal digits (Niven number). - C#: sum digits in a loop, then
original % sum == 0. - Classic demo:
18is Harshad;11is not.
Did you know?
A Harshad number is also called a Niven number. The name comes from the Sanskrit word harsha, meaning joy. Every single-digit positive integer from 1 through 9 is Harshad, because the number equals the sum of its only digit.
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