One-Digit Number is Harshad

Theorem
Let $n$ be a $1$-digit positive integer.

Then $n$ is a harshad number.

Proof
By definition, a harshad number is divisible by the sum of its digits base $10$.

Let $n$ be a $1$-digit positive integer.

The sum of the digits of $n$ is trivially $n$.

The result follows from Integer Divides Itself.