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1. en.wikipedia.org › wiki › Harshad_numberHarshad number - Wikipedia

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   In 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. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. [1]

2. www.geeksforgeeks.org › harshad-or-niven-numberHarshad (Or Niven) Number - GeeksforGeeks

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   Sep 11, 2023 · Learn what a Harshad number is, how to check if a number is a Harshad number in different bases, and see examples and code in various languages. A Harshad number is an integer divisible by the sum of its digits in the same base.

3. www.javatpoint.com › program-to-check-harshad-numberProgram to determine whether a given number is a Harshad ...

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   A Harshad number is a number that is divisible by the sum of its digits. Learn the definition, algorithm and examples of Harshad number, and write a program in Python, C, Java and PHP to find out if a given number is a Harshad number.

4. People also ask

   What is an all-harshad number?

   • Define an all-Harshad (or all-Niven) number as a positive integer which is divisible by the sum of its digits in all bases . Then only 1, 2, 4, and 6 are all-Harshad numbers. Cai, T. "On 2-Niven Numbers and 3-Niven Numbers." Fib. Quart. 34, 118-120, 1996. Cooper, C. N. and Kennedy, R. E. "Chebyshev's Inequality and Natural Density."

   Harshad Number -- from Wolfram MathWorld

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   Is 156 a Harshad number?

   • For example, if number is 156, then sum of its digit will be 1 + 5 + 6 = 12. Since 156 is divisible by 12. So, 156 is a Harshad number. To find whether the given number is a Harshad number or not, calculate the sum of the digit of the number then, check whether the given number is divisible by the sum of its digit.

   Program to determine whether a given number is a Harshad number

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   What is a -Harshad number?

   • Grundman (1994) defined an -Harshad (or -Niven) number to be a positive integer which is divisible by the sum of its digits in base . Cai (1996) showed that for or 3, there exists an infinite family of sequences of consecutive -Harshad numbers of length .

   Harshad Number -- from Wolfram MathWorld

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   Is 12 a Harshad number?

   • The number 12 is a harshad number in all bases except octal . The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9. The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).

   Harshad number - Wikipedia

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5. mathworld.wolfram.com › HarshadNumberHarshad Number -- from Wolfram MathWorld

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   4 days ago · Harshad Number. A positive integer which is divisible by the sum of its digits, also called a Niven number (Kennedy et al. 1980) or a multidigital number (Kaprekar 1955). The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, ... (OEIS A005349 ).

6. planetmath.org › HarshadNumberHarshad number - PlanetMath.org

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   When an integer is divisible by the sum of its digits, it’s called a Harshad number or Niven number. That is, given m is the number of digits of n and d is an integer of n, m ∑ i=1di|n ∑ i = 1 m d i | n. All 1-digit numbers and the base number itself are Harshad numbers. 1, 2, 4 and 6 are always Harshad numbers regardless of the base.

   • Canonical name: HarshadNumber
   • Last modified on: 2013-03-22 15:47:04

   • Date of creation: 2013-03-22 15:47:04
   • Title: Harshad number

7. www.numbersaplenty.com › set › Harshad_numberHarshad numbers

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   A number is a Harshad (also called Niven) number if it is divisible by the sum of its digits. For example, 666 is divisible by 6+6+6 so it is a Harshad number.

8. archive.lib.msu.edu › crcmath › mathHarshad Number

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   May 25, 1999 · A Harshad number is a positive integer that is divisible by the sum of its digits. Learn about the properties, sequences and references of Harshad numbers, also known as Niven numbers, in this web page.