In this post we are going to learn about the **criteria of divisibility by 3, 4, 9 and 11**.

**Criteria of divisibility by 3**

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

For example: **Is 1098 divisible by 3?**

We add all the digits of 1098:

1 + 0 + 9 + 8 = 18

1+ 8 = 9

9 is a multiple of 3, therefore 1098 is divisible by 3.

**Criteria of divisibility by 4**

A number is divisible by 4 when the last two numbers are divisible by 4.

Let’s look at an example. **We want to know if 448 is divisible by 4**, so we need to see if its last two numbers, 48, are divisible by 4.

48/4 = 12 and the remainder is 0.

Therefore, 448 is divisible by 4.

**Criteria of divisibility by 9**

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

For example, **let’s check if 2610 is a multiple of 9.**

2 + 6 + 1 + 0 = 9

Therefore 2610 is divisible by 9.

**Criteria of divisibility by 11**

A number is divisible by 11 when the sum of the numbers that occupy the even places minus the sum of the numbers that occupy the odd places is equal to 0 or a number which is a multiple of 11.

**Is 5863 divisible by 11?**

To find out if 5863 is divisible by 11, we identify which numbers are located in the even places and which numbers are located in the odd places.

Even places: 8 and 3.

We add them: 8 + 3 = 11

Odd places: 5 and 6.

We add them: 5 + 6 = 11

11-11 = 0

Therefore 5863 is divisible by 11.

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Learn More:

- Follow the Divisibility Guidelines for 3
- Divisibility Guidelines for 6 and Some Examples
- Divisibility Guidelines for 9 and Some Examples
- Learn the Criteria for the Divisibility of 5
- Divisibility Guidelines for 6, 8 and 12

- Robby’s New Laboratory. What are Variables in Coding? - 10/05/2020
- Learn Everything About the Properties of Powers - 05/18/2020
- Diagnostic Questions in Mathematics Education - 05/11/2020

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