Harshad Number Checker
Check whether a number is a Harshad (Niven) number, divisible by the sum of its own digits.
Last reviewed by the Radiatus Cloud team
Check whether a number is a Harshad (Niven) number.
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Check for a Harshad number
A Harshad number, also called a Niven number, is a positive integer that is divisible by the sum of its own digits. This checker adds up the digits and tests whether the number divides evenly by that sum. For example, eighteen is a Harshad number because its digits add to nine, and eighteen divided by nine is exactly two. The name Harshad comes from the Sanskrit for great joy, given by the mathematician D. R. Kaprekar.
The tool shows the digit sum and the division so you can see why a number qualifies.
Numbers divisible by their digit sum
Harshad numbers are fairly common among small integers, and every single-digit number is a Harshad number since it is divisible by itself. They have interesting distribution properties and connect to other recreational number categories. All multiples of nine are Harshad numbers, because their digit sum is itself a multiple of nine, which divides them. Exploring them is a gentle introduction to divisibility and digit-based number properties.
The property depends on the base, so a number can be Harshad in base ten but not in another base. All calculation happens locally in your browser.
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Frequently Asked Questions
What is a Harshad number?
A positive integer divisible by the sum of its digits, such as eighteen, whose digits add to nine, which divides eighteen.
Why is it also called a Niven number?
Niven number is an alternative name, after the mathematician Ivan Niven, for the same property of divisibility by the digit sum.
Are all multiples of nine Harshad numbers?
Yes. Their digit sum is a multiple of nine, which divides the number, so every multiple of nine is a Harshad number.
Does the base matter?
Yes. The property depends on the number base, so a Harshad number in base ten may not be one in another base.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter a positive integer to check if it is a Harshad number.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.