Definition:Harshad Number

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 base $10$.

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

It was described by D.R. Kaprekar.

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

 * Niven numbers
 * All-Harshad numbers