Harshad number

noun

A positive integer which is divisible by the sum of all of its digits.

“The sum of digits of 24 is 2 + 4 = 6, and 24 is divisible by 6, so 24 is a Harshad number.”

Similar
Niven number
OriginSanskrit हर्षद →
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Meanings

nounHarshad number (plural Harshad numbers)

plural Harshad numbers

  1. mathematicsA positive integer which is divisible by the sum of all of its digits.

    The sum of digits of 24 is 2 + 4 = 6, and 24 is divisible by 6, so 24 is a Harshad number.

    Synonyms: Niven number

Synonyms & antonyms

nounA positive integer which is divisible by the sum of all of its digits.

Similar
Niven number
Also see
niven number

Origin

  1. Sanskritहर्षद“giving joy”
  2. EnglishHarshad number

Coined by Indian recreational mathematician D. R. Kaprekar, from Sanskrit हर्षद (harṣada, “giving joy”). The capitalization is likely based on mathematicians' incorrect assumption that harshad is a proper noun.

More words from Sanskrit

Full word history & related roots →

Translations

Italian numero di Harshad
  • numero di HarshadTranslations
Spanish número Harshad
  • número HarshadTranslations
Cite this entry
APA

Harshad number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Harshad%20number

MLA

“Harshad number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Harshad%20number. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Harshad number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Harshad%20number.

Source: Harshad number on Wiktionary, CC BY-SA 4.0.