Divisibility rules

key notes:

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

💡Tip💡
A number will always be divisible by its factors. Since 2 is a factor of 12, we know 12 is divisible by 2.

Divisibility rules

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

2A number is divisible by 2 if its ones digit is 0, 2, 4, 6, or 8.
3A number is divisible by 3 if the sum of its digits is divisible by 3.
4A number is divisible by 4 if the number formed by its last 2 digits is divisible by 4.
5A number is divisible by 5 if its ones digit is 0 or 5.
6A number is divisible by 6 if it is divisible by both 2 and 3.
8A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.
9A number is divisible by 9 if the sum of its digits is divisible by 9.
10A number is divisible by 10 if its ones digit is 0.

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.

Learn with an example

🗼 Type a digit that makes this statement true.

645,02 _____ is divisible by 2.

  • Yes
  • no

Since the number 645,02 ? is divisible by 2, the missing digit must be 0, 2, 4, 6, or 8.

🗼 Type a digit that makes this statement true.

50,515,51 _____ is divisible by 10.

  • yes
  • no

Since the number 50,515,51 ? is divisible by 10, the missing digit must be 0.

🗼Is 6,487,572 divisible by 10?

  • yes
  • no
  • Try the “divisible by 10” rule on 6,487,572.
  • Look at the ones digit:
  • 6,487,572
  • The ones digit is 2. 
    The rule says that 6,487,572 is not divisible by 10.

let’s practice: