Divisibility rules

​What is divisibility?

​If you can divide two numbers without a remainder, then the first number is divisible by the second.
For example, 12 is divisible by 2.
12÷2=6

But 12 is not divisible by 5. When you divide 12 by 5, you get a remainder.
12÷5=2 R2

​Divisibility rules

​Divisibility rules can help you easily decide if a number is divisible by another number. This table shows some common divisibility rules.

​Try it! See the examples below.

​Divisibility by 2
A number is divisible by 2 if its ones digit is 0, 2, 4, 6, or 8.
Is 346 divisible by 2?
The ones digit in 346 is 6.
So, 346 is divisible by 2.

Is 223 divisible by 2?
The ones digit in 223 is 3.
So, 223 is not divisible by 2.

​Divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Is 324 divisible by 3?
Add the digits. 3+2+4=9
Since 9 is divisible by 3, we know 324 is divisible by 3.

Is 412 divisible by 3?
Add the digits. 4+1+2=7
Since 7 is not divisible by 3, we know 412 is not divisible by 3.

​Divisibility by 4
A number is divisible by 4 if the number formed by its last 2 digits is divisible by 4.
Is 536 divisible by 4?
The last 2 digits of 536 form the number 36.
Since 36 is divisible by 4, we know 536 is divisible by 4.

Is 247 divisible by 4?
The last 2 digits of 247 form the number 47.
Since 47 is not divisible by 4, we know 247 is not divisible by 4.

​Divisibility by 5
A number is divisible by 5 if its ones digit is 0 or 5.
Is 635 divisible by 5?
The ones digit in 635 is 5.
So, 635 is divisible by 5.

Is 513 divisible by 5?
The ones digit in 513 is 3.
So, 513 is not divisible by 5.

​Divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3.
Is 348 divisible by 6?
348 is even, so it is divisible by 2.
Add the digits. Since 3+4+8=15, it is divisible by 3.
Since 348 is divisible by both 2 and 3, it is also divisible by 6.

Is 212 divisible by 6?
212 is even, so it is divisible by 2.
Add the digits. Since 2+1+2=5, it is not divisible by 3.
So, 212 is not divisible by 6.

​Divisibility by 8
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.
Is 1,016 divisible by 8?
The last 3 digits form the number 016, or 16.
16 is divisible by 8, so 1,016 is divisible by 8.

Is 1,231 divisible by 8?
The last 3 digits form the number 231.
231 is not divisible by 8, so 1,231 is not divisible by 8.

​Divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Is 675 divisible by 9?
Add the digits. 6+7+5=18
18 is divisible by 9, so 675 is divisible by 9.

Is 364 divisible by 9?
Add the digits.
3+6+4=13 13 is not divisible by 9, so 364 is not divisible by 9.

​Divisibility by 10
A number is divisible by 10 if its ones digit is 0.
Is 420 divisible by 10?
The ones digit in 420 is 0.
So, 420 is divisible by 10.

Is 317 divisible by 10?
The ones digit in 317 is 7.
So, 317 is not divisible by 10.