Skill: Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10

Divisibility means a number can be divided evenly, with no remainder. Use these rules:

• 2: The ones digit is even: $(0,2,4,6,)$ or $8$.
• 3: The sum of the digits is divisible by $3$.
• 4: The last two digits form a number divisible by $4$.
• 5: The ones digit is $0$ or $5$.
• 6: The number is divisible by both $2$ and $3$.
• 9: The sum of the digits is divisible by $9$.
• 10: The ones digit is $0$.

Example: Determine which of these numbers divide $(2{,}736)$ evenly: $(2,3,4,5,6,9,)$ and $(10)$.

1. Check $2$: The ones digit is $6$, which is even.
   So, $(2{,}736)$ is divisible by $2$.

2. Check $3$ and $9$: Add the digits:

$$2+7+3+6=18$$

Since $(18)$ is divisible by both $3$ and $9$, $(2{,}736)$ is divisible by both $3$ and $9$.

3. Check $4$: Look at the last two digits, $(36)$. Since $(36)$ is divisible by $4$, $(2{,}736)$ is divisible by $4$.

4. Check $5$: The ones digit is $6$, not $0$ or $5$.
   So, $(2{,}736)$ is not divisible by $5$.

5. Check $6$: The number is divisible by both $2$ and $3$, so it is divisible by $6$.

6. Check $(10)$: The ones digit is not $0$.
   So, $(2{,}736)$ is not divisible by $(10)$.

Therefore, $(2{,}736)$ is divisible by

$$\boxed{2,3,4,6,\text{ and }9}$$

but not by $5$ or $(10)$.