1. **Stating the problem:** Prove that an even number is divisible by 2. 2. **Definition:** An even number is any integer that can be written as $2k$ where $k$ is an integer. 3. **Formula used:** Even number $= 2k$, where $k \in \mathbb{Z}$. 4. **Proof:** - Let $n$ be an even number. - By definition, $n = 2k$ for some integer $k$. - Dividing $n$ by 2 gives: $$\frac{n}{2} = \frac{2k}{2}$$ - Simplify the fraction: $$\frac{\cancel{2}k}{\cancel{2}} = k$$ - Since $k$ is an integer, $\frac{n}{2}$ is an integer. 5. **Conclusion:** Since $\frac{n}{2}$ is an integer, $n$ is divisible by 2, which proves that $n$ is even. This completes the proof that an even number is divisible by 2.