---
tag: GK281PC7QT
kind: concept
name: Harshad number
aliases: [all-harshad-number, all-niven-number, boscaro-number, boscaro-numbers, consecutive-harshad-numbers, harshad-numbers, harshadmorphic-number, multiple-harshad-number, multiple-harshad-numbers, n-harshad-number, n-niven-number, niven-number, niven-numbers, nivenmorphic-number]
sources:
  - wikipedia: en:641307@r1367147024
    locator: Harshad number
    note: adopted
    mention: wikipedia://en/641307
    sections: [Summary]
same_as:
  wikidata: Q375355
  wikipedia: Harshad number
inventory: [KR2T0GCH18]
---

## Summary

In recreational mathematics, a **Harshad number** (or **Niven number**) in a given number base is an [[integer|0C4JS9RF5M]] that is divisible by the sum of its digits when written in that base. Harshad numbers in base $n$ are also known as **$n$-harshad** (or **$n$-Niven**) numbers. Because being a harshad number is determined according to the base the number is expressed in, a number can be a Harshad number many times over. So-called **Trans-harshad numerals** are sequences of the digits 0-9 which, in every base which uses all their digits, represent a Harshad number in that base.