Skill: Use divisibility rules for 2, 3, 5, 9, and 10

A number is divisible by another number if it can be divided evenly, with no remainder.

Use these rules:

• Divisible by 2: The ones digit is even: $0,2,4,6,$ or $8$.
• Divisible by 3: The sum of the digits is divisible by $3$.
• Divisible by 5: The ones digit is $0$ or $5$.
• Divisible by 9: The sum of the digits is divisible by $9$.
• Divisible by 10: The ones digit is $0$.

Worked example

Which of $2,3,5,9,$ and $10$ divide $4{,}350$ evenly?

Step 1: Test divisibility by $2$.

The ones digit of $4{,}350$ is $0$. Since $0$ is even, $4{,}350$ is divisible by $2$.

Step 2: Test divisibility by $3$ and $9$.

Add the digits:

$$4+3+5+0=12$$

Since $12$ is divisible by $3$, $4{,}350$ is divisible by $3$.

Since $12$ is not divisible by $9$, $4{,}350$ is not divisible by $9$.

Step 3: Test divisibility by $5$.

The ones digit is $0$, so $4{,}350$ is divisible by $5$.

Step 4: Test divisibility by $10$.

The ones digit is $0$, so $4{,}350$ is divisible by $10$.

Therefore, $4{,}350$ is divisible by

$$2,\ 3,\ 5,\text{ and }10,$$

but it is not divisible by $9$.