Fizz Buzz - Insight

A number is divisible by $3$ if $i \bmod 3 = 0$. A number is divisible by $5$ if $i \bmod 5 = 0$. Both conditions use modulo to check divisibility.

The tricky part is the order of checks. You must check divisibility by both $3$ and $5$ first. If you check $3$ first and return "Fizz", you never get to check $5$.

For $i = 15$, both $15 \bmod 3 = 0$ and $15 \bmod 5 = 0$ are true, so you output "FizzBuzz".