Harshad Number: A Number is Divisible by its Digit Sum, an Divisibility Approach by Considering the Digit-sum to be Seven

Harshad Number: A Number is Divisible by its Digit Sum, an Divisibility Approach by Considering the Digit-sum to be Seven

Banashree Sen ^a,b, Tarit Kr Majumder^b, Payal Sen^b

^(a) Department of Commerce and Management, St. Xavier’s University, Newtown-700160, WB, India

^(b) Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata-741249, WB, India

Email:  banashreesen7@gmail.com

Abstract: A Harshad number, also known as a Niven number, is a positive integer that is divisible by the sum of its digits. In other words, if one can add up all the digits of that number and divide the number by that sum, the result will be a whole number. We will exclude the trivial cases where the summative number itself present in that digit; otherwise in most of the cases the number will follow the properties of Harshad number[1,2]. In this article, excluding the trivial cases, we tried to extend our concept which usually maintained in Harshad number, in an advanced way. The advanced concept of Harshad number deals with such kind of expression of the digits where the summative result of combined digit will not be present anywhere. This type of number also known as Harshad number [1,3] with an exclusion of total non-minor cases. This type of number does not occur in units, tens but in hundreds if the choice of digit sums chosen to be seven. For the choice of division factor[2,4] to be 7 we take trial and error method pertaining the outcome to be a non-trivial and non-containing digit sum number. The first digit of this kind satisfies in hundred places and the number in particular is 322. We also found that the next such number is next appearing in thousand digits and that is 1016. And such kind of number used to maintain in a sequential manner. We also tried to exhibit the pattern of Harshad [1,2,3] Sequence in our article.

Keywords: Harshad Number (HN), Digit-Sum, Divisibility.