Skip to content
EntityQ375355· pop 30· linked from 285 articles

harshad number

Sign in to save

Also known as Niven number

integer that is divisible by the sum of its digits

Wikidata facts

Named after
Ivan M. Niven
Show 3 more facts
facet of
digit sum
significant person
D. R. Kaprekar
maintained by WikiProject
WikiProject Mathematics
Sources (2)

via Wikidata · CC0

~13 min read

Encyclopedic overview

In recreational mathematics, a harshad number (or Niven number) in a given number base is an integer 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.

Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977.

Excerpted from Wikipedia’s “harshad number” article, available under the CC BY-SA 4.0 licence.