# What is Divisibility in Math?

## Divisibility

The four basic functions of arithmetic, or the study of numbers, are addition, subtraction, multiplication, and division. This lesson will focus on division.

In a division problem, there are three important numbers: the **dividend**, the **divisor**, and the **quotient**. The dividend is divided by the divisor to get the quotient. For example,

{eq}12 \div 3 = 4 {/eq}

In this problem, 12 is the dividend, 3 is the divisor, and 4 is the quotient. Twelve is divided by 3 to get 4; in other words, 12 is divisible by 3.

But what does it mean for a number to be **divisible**? A number is divisible by another number when it can be split equally into parts of that amount with no **remainder**. A remainder in division is a value left over when the dividend is not divisible by the divisor.

In the above example, 12 can be split into 4 equal parts of 3. This can be proven by adding 3 together 4 times: 3 + 3 + 3 + 3 = 12.

## Divisibility

What is divisibility? **Divisibility** is being able to be divided equally by a certain number. Think of sharing a bunch of candies that you have with your friends. If you have 3 friends and 3 candies, then you can give each friend 1 candy. Everyone gets an equal share. In math, we call this divisibility by 3. If you can't give your friends an equal share, then we say we don't have divisibility by 3.

We also use the word 'divisible.' We will usually say that something is divisible by something else. So, we will say that 3 is divisible by 3 because you can divide 3 candies by 3 friends equally. Remember what the symbol looks like for division? Yes, it is a horizontal line with a dot on top and a dot on the bottom. In this video lesson, we will look at what numbers can be divided by 2, 3, and 4. Are you ready to begin?

## Numbers Divisible by 2

When numbers are divisible by 2, they can be divided equally by 2 with no remainder. Luckily, there is a **divisibility test** that can be performed to check whether a number is divisible by 2, no matter how small or large it is. If the number passes the test, it can be divided by 2!

According to the divisibility test, all **even numbers** are divisible by 2. Even numbers end in 0, 2, 4, 6, or 8. This means that 0, 2, 4, 6, and 8 are all divisible by 2. Additionally, any number that ends in 0, 2, 4, 6, or 8 is also divisible by 2.

Here are some examples:

#### Use the divisibility test to determine if 4,823 is divisible by 2.

The number 4,823 ends in 3, which is not an even number. Therefore, 4,823 is not divisible by 2.

#### Use the divisibility test to determine if 106 is divisible by 2.

The number 106 ends in 6, which is an even number. Therefore, 106 is divisible by 2.

## Numbers Divisible by 3

Numbers that are divisible by 3 can be split into equal parts of 3 with no remainder, like 12 in the earlier example. Other numbers divisible by 3 include 9, 15, 18, 21, and so on.

### How to Know if a Number is Divisible by 3

Just like with 2, there is a divisibility test to determine whether a number is divisible by 3. This test is a bit more complicated than the test for divisibility by 2, though.

To find whether a number is divisible by 3, first add all the **digits** of the number. Digits are the individual numbers from 0 to 9 that make up the larger number.

Once the sum is found, check to see if the sum is divisible by 3. If the sum is divisible by 3, the original number will be, too. If the sum is not divisible by 3, the original number won't be, either.

To test this rule, here are some examples:

#### Use the divisibility test to determine whether 90,354 is divisible by 3.

First, add the digits of the number 90,354 together. 9 + 0 + 3 + 5 + 4 = 21.

21 is divisible by 3. Therefore, 90,354 is also divisible by 3.

#### Use the divisibility test to determine whether 104,789,332 is divisible by 3.

First, add the digits of the number 104,789,332 together. 1 + 0 + 4 + 7 + 8 + 9 + 3 + 3 + 2 = 37.

37 is not divisible by 3. Therefore, 104,789,332 is also not divisible by 3.

## Numbers Divisible by 4

A number that is divisible by 4 can be split into equal parts of 4 with no remainder. Examples of numbers divisible by 4 include 8, 16, 20, 24, and more. Like with 2 and 3, there is a test to check whether a number is divisible by 4.

### How to Tell if a Number is Divisible by 4

To check whether a large number is divisible by 4, look at its last two digits. Take them away from the larger number to form a new number. If the new number is divisible by 4, the larger number will be, too.

Here are some examples of this rule in action:

#### Use the divisibility test to determine whether 616 is divisible by 4.

The last two digits of 616 are 1 and 6, or 16. The number 16 is divisible by 4. This means that 616 is also divisible by 4.

#### Use the divisibility test to determine whether 3,723 is divisible by 4.

The last two digits of 3,723 are 2 and 3, or 23. The number 23 is not divisible by 4. This means that 3,723 is not divisible by 4.

## Lesson Summary

In a division equation, there are three numbers. The **dividend** is the number being divided, the **divisor** is the number doing the dividing, and the **quotient** is the answer to the problem. A number is said to be **divisible** by another number if it can be divided by the other number evenly, with no **remainder** left over. There are several **divisibility tests** that can be used to quickly check whether a large number is divisible by a specific divisor. These tests require examination of the **digits**, or numbers 0 through 9, that make up the larger number. The divisibility tests discussed in this lesson are the following:

To test if a number is divisible by 2, check if its last digit is an **even number**. Even numbers are 0, 2, 4, 6, and 8. If the last digit is an even number, the number is divisible by 2.

To test if a number is divisible by 3, add all the digits of the number and check if the sum is divisible by 3. If the sum is divisible by 3, the larger number is also divisible by 3.

To test if a number is divisible by 4, take the last two digits in the number to make a new number. If the new number is divisible by 4, the original number is as well.

## By 2

Let's stick to our sharing candies with friends example. In this case, divisibility by 2; we have 2 friends that we want to share candies with. Can you think of a number of candies that can be divided equally between these two friends? Is it 2? Yes, if you have 2 candies, you can definitely share the 2 candies equally between your 2 friends.

How many candies would each friend get? 1. So, 2 is divisible by 2, and 2 divided by 2 equals 1 since that is the number of candies that each friend got. Think of splitting the number of candies you have evenly into 2 groups. If you can do that, then the number is divisible by 2.

What's another number that is divisible by 2? Let's try 4. How can you divide four candies equally between 2 friends? Each friend can get 2 candies. So, we have 4 divided by 2 is 2. What other numbers have divisibility by 2? 6, 8, 10, 12, and so on. Do you see a pattern? Yes, each number is the previous number plus 2. You can continue this pattern to find even more numbers that are divisible by 2.

## By 3

Let's continue on to the number 3. Now you have 3 friends. How many candies do you need so that you can share them equally between your friends? The first number is 3, since this means that each friend will get 1 candy each. So, 3 is divisible by 3. 3 divided by 3 is 1.

What's another number? 6. How many candies will each friend get? The answer is 2. So, 6 is divisible by 3. 6 divided by 3 is 2. What other numbers are there? 9, 12, 15, 18, and so on. Do you see a pattern here, too? Yes, it is very similar to the pattern for divisibility by 2, except now we are adding 3 to each previous number.

## By 4

Now, what about divisibility by 4? What do you think the pattern will be? Will it be 4, 8, 12, 16, and so on? Yes, you are right! We start with our first number that can be divided equally between 4 friends, 4 candies, and then we continue by adding 4 to each previous number. 4 divided by 4 is 1. 8 divided by 4 is 2. 12 divided by 4 is 3. And the pattern continues.

## Lesson Summary

What did we learn? We learned that **divisibility** means being able to be divided equally by a certain number. In math, we also use the word 'divisible.' When we say 12 is divisible by 4, it means that we can split 12 candies evenly between 4 friends. In this video lesson, we saw the numbers that are divisible by 2, 3, and 4. We learned that they all have a pattern.

For divisibility by 2, we start with the number 2 and then continue by adding 2 to each previous number. We get 2, 4, 6, 8, 10, etc. For divisibility by 3, we start with 3 and then we keep adding 3 to each previous number. We get 3, 6, 9, 12, etc. For divisibility by 4, we begin with 4 and then continue adding 4 to each previous number. We get 4, 8, 12, 16, etc.

## Learning Outcomes

After this lesson is done you should be able to:

- State the meaning of
*divisibility* - Recall how to find the divisibility patterns for 2, 3 and 4

To unlock this lesson you must be a Study.com Member.

Create your account

## Divisibility

What is divisibility? **Divisibility** is being able to be divided equally by a certain number. Think of sharing a bunch of candies that you have with your friends. If you have 3 friends and 3 candies, then you can give each friend 1 candy. Everyone gets an equal share. In math, we call this divisibility by 3. If you can't give your friends an equal share, then we say we don't have divisibility by 3.

We also use the word 'divisible.' We will usually say that something is divisible by something else. So, we will say that 3 is divisible by 3 because you can divide 3 candies by 3 friends equally. Remember what the symbol looks like for division? Yes, it is a horizontal line with a dot on top and a dot on the bottom. In this video lesson, we will look at what numbers can be divided by 2, 3, and 4. Are you ready to begin?

## By 2

Let's stick to our sharing candies with friends example. In this case, divisibility by 2; we have 2 friends that we want to share candies with. Can you think of a number of candies that can be divided equally between these two friends? Is it 2? Yes, if you have 2 candies, you can definitely share the 2 candies equally between your 2 friends.

How many candies would each friend get? 1. So, 2 is divisible by 2, and 2 divided by 2 equals 1 since that is the number of candies that each friend got. Think of splitting the number of candies you have evenly into 2 groups. If you can do that, then the number is divisible by 2.

What's another number that is divisible by 2? Let's try 4. How can you divide four candies equally between 2 friends? Each friend can get 2 candies. So, we have 4 divided by 2 is 2. What other numbers have divisibility by 2? 6, 8, 10, 12, and so on. Do you see a pattern? Yes, each number is the previous number plus 2. You can continue this pattern to find even more numbers that are divisible by 2.

## By 3

Let's continue on to the number 3. Now you have 3 friends. How many candies do you need so that you can share them equally between your friends? The first number is 3, since this means that each friend will get 1 candy each. So, 3 is divisible by 3. 3 divided by 3 is 1.

What's another number? 6. How many candies will each friend get? The answer is 2. So, 6 is divisible by 3. 6 divided by 3 is 2. What other numbers are there? 9, 12, 15, 18, and so on. Do you see a pattern here, too? Yes, it is very similar to the pattern for divisibility by 2, except now we are adding 3 to each previous number.

## By 4

Now, what about divisibility by 4? What do you think the pattern will be? Will it be 4, 8, 12, 16, and so on? Yes, you are right! We start with our first number that can be divided equally between 4 friends, 4 candies, and then we continue by adding 4 to each previous number. 4 divided by 4 is 1. 8 divided by 4 is 2. 12 divided by 4 is 3. And the pattern continues.

## Lesson Summary

What did we learn? We learned that **divisibility** means being able to be divided equally by a certain number. In math, we also use the word 'divisible.' When we say 12 is divisible by 4, it means that we can split 12 candies evenly between 4 friends. In this video lesson, we saw the numbers that are divisible by 2, 3, and 4. We learned that they all have a pattern.

For divisibility by 2, we start with the number 2 and then continue by adding 2 to each previous number. We get 2, 4, 6, 8, 10, etc. For divisibility by 3, we start with 3 and then we keep adding 3 to each previous number. We get 3, 6, 9, 12, etc. For divisibility by 4, we begin with 4 and then continue adding 4 to each previous number. We get 4, 8, 12, 16, etc.

## Learning Outcomes

After this lesson is done you should be able to:

- State the meaning of
*divisibility* - Recall how to find the divisibility patterns for 2, 3 and 4

To unlock this lesson you must be a Study.com Member.

Create your account

#### What is it called when a number is divisible by 2?

When a number is divisible by 2, it is an even number. Even numbers include 0, 2, 4, 6, and 8, along with any larger number that ends in 0, 2, 4, 6, or 8.

#### Are all numbers that end in 4 divisible by 4?

Not all numbers that end in 4 are divisible by 4. Examples of numbers ending in 4 that cannot be divided equally by 4 are 14, 34, and 54.

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