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What is a Harshad number?
Is 1729 a Harshad number?
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]
Sep 11, 2023 · An integer number in base 10 which is divisible by the sum of its digits is said to be a Harshad Number. An n-Harshad number is an integer number divisible by the sum of its digit in base n. Below are the first few Harshad Numbers represented in base 10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20……… Given a number in base 10, our task is ...
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. C.Cooper & R.E.Kennedy proved that it is possible to have at most 20 consecutive Niven numbers and this happens infinitely often.
A Harshad number (also called Niven number) is a natural number that is divisible by the sum of its digits. Obviously, 1-digit numbers are all Harshad numbers. For example, Is 115 a Harshad number? First, calculate the sum of its digits. 1 + 1 + 5 = 7. Second, determine whether it is divisible. 115 ÷ 7 = 15. The answer is an integer.
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 ).
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.
Sep 6, 2017 · A base Harshad number is a positive integer that is divisible by the sum of its base digits. For example, in the decimal numeral system, 1729 is a Harshad number since 1 + 7 + 2 + 9 = 19, and 1729 = 19 × 91.
