Definition:Harshad Number

Definition
A Harshad number is a positive integer which is divisible by the sum of its digits base $10$.

Hence a Harshad number can be defined as being a Niven number [Definition:Decimal Notation|base $10$]].

The name comes from the Sanskrit word हर्ष (harṣa + da), which means giving joy.

It was described by.

Clearly all numbers of one digit are Harshad.

The first few Harshad numbers are:


 * $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, \ldots$

Also see

 * Definition:Niven Number
 * Definition:All-Harshad Number