Number of form 28000...0007 is Divisible by 7/Proof 2

Theorem

Let $x$ be a natural number in the form:

$\sqbrk {28 \underbrace {000 \cdots 0}_n 7}_{10}$

Then $x$ is divisible by $7$.

Proof

We have:

\(\ds \sqbrk {28 \underbrace {000 \cdots 0}_n 7}_{10}\)

\(=\)

\(\ds 7 \times \sqbrk {4 \underbrace {000 \cdots 0}_n 1}_{10}\)

and the result follows by definition of divisibility.

$\blacksquare$