06-21-2026, 01:03 PM
Harshad number
Summary
A Harshad number (or Niven number) is a positive integer that is divisible by the sum of its own digits. For example, 18 is a Harshad number because its digits add up to 1 + 8 = 9, and 18 is divisible by 9. The concept was introduced by the Indian mathematician D. R. Kaprekar and has been studied in number theory due to its interesting patterns and properties.
Harshad numbers exist in every base, not only decimal, and their distribution has been explored through various mathematical results. Some well-known examples include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 18, while numbers like 11 are not Harshad because 11 is not divisible by 1 + 1 = 2. These numbers illustrate the connection between digit-based properties and divisibility in mathematics.
ARTICLE
Summary
A Harshad number (or Niven number) is a positive integer that is divisible by the sum of its own digits. For example, 18 is a Harshad number because its digits add up to 1 + 8 = 9, and 18 is divisible by 9. The concept was introduced by the Indian mathematician D. R. Kaprekar and has been studied in number theory due to its interesting patterns and properties.
Harshad numbers exist in every base, not only decimal, and their distribution has been explored through various mathematical results. Some well-known examples include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 18, while numbers like 11 are not Harshad because 11 is not divisible by 1 + 1 = 2. These numbers illustrate the connection between digit-based properties and divisibility in mathematics.
ARTICLE
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