Phrase guide

Harshad number

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

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

Meaning relationships

Synonyms: Niven number

Antonyms: none provided

History

Etymology

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.

Across languages

Translations

2 source translations are retained for this English entry.

  • Italian: numero di Harshad — Translations
  • Spanish: número Harshad — Translations