# Divisibility Rules for 3, 6 and 9 - Examples, Exercises and Solutions

### Divisibility criteria for$3$,$6$ and$9$

#### Divisibility criteria for$3$

A number is divisible by $3$ if the sum of its digits is a multiple of $3$.

#### Divisibility criteria for$6$

A number is divisible by $6$ if it is even and also a multiple of $3$.

#### Divisibility criteria for$9$

A number is divisible by $9$ if the sum of its digits is a multiple of $9$.

## Examples with solutions for Divisibility Rules for 3, 6 and 9

### Exercise #1

Determine if the following number is divisible by 3:

$352$

No

### Exercise #2

Determine if the following number is divisible by 3:

$673$

No

### Exercise #3

Will a number divisible by 6 necessarily be divisible by 2?

Yes

### Exercise #4

Determine if the following number is divisible by 3:

$132$

Yes

### Exercise #5

Determine if the following number is divisible by 3:

$564$

Yes

### Exercise #6

Will a number divisible by 9 necessarily be divisible by 6?

No

### Exercise #7

Will a number divisible by 3 necessarily be divisible by 6?

No

### Exercise #8

Will a number divisible by 3 necessarily be divisible by 9?

No

### Exercise #9

Will a number divisible by 2 necessarily be divisible by 6?

No

### Exercise #10

Is the number below divisible by 9?

$987$

No

### Exercise #11

Is the number below divisible by 9?

$685$

No

### Exercise #12

Will a number divisible by 9 necessarily be divisible by 3?

Yes

### Exercise #13

Is the number below divisible by 9?

$189$

Yes

### Exercise #14

Is the number below divisible by 9?

$999$

Yes

### Exercise #15

Determine if the following number is divisible by 6:

$681$