Divisibility Rules for 2, 4, and 10

Divisibility Criteria for 2

A number is divisible by $2$ if the units digit is even - that is, it divides by $2$ without a remainder.

Divisibility Rules for 4

First way: A number is divisible by $4$ if its last two digits are divisible by $4$ .
Second way: Multiply the tens digit by $2$ and add the units digit. If the result obtained is a multiple of $4$ , then the original number is as well.

Divisibility Rules for 10

A number is divisible by $10$ if its units digit is $0$ .

Detailed explanation

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Is the number 10 divisible by 4?

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Divisibility Rules for 2, 4, and 10

In this article, we will teach you the best and simplest tricks to identify if a number is divisible by $2$ , by $4$ , and by $10$ .

Shall we start?

Divisibility Rules for 2

A number is divisible by $2$ if its units digit is even.
Let's remember that an even digit is one that can be divided by $2$ without leaving a remainder.
If the units digit is odd, we can determine, without a doubt, that the number is not divisible by $2$ .

Divisibility by 2 - example 1
The number $48$
Let's observe the units digit $8$
$8$ is even, therefore, we can determine that the number $48$ is divisible by $2$ .

Divisibility by 2 - example 2
The number $677$
Let's observe the units digit $7$ .
$7$ is odd, therefore, we can determine that $677$ is not divisible by $2$ .

Divisibility by 2 - example 3
Determine if the number $3578$ is divisible by $2$ .

Solution:
The units digit is $8$ , even, therefore, the number is divisible by $2$ .

Divisibility by 2 - example 4

Determine if the number $10003$ is divisible by $2$

Solution:
The units digit is $3$ , odd, therefore, the number is not divisible by $2$ .

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Test your knowledge

Question 1

Is the number 15 divisible by 2?

Question 2

Is the number 60 divisible by 10?

Question 3

Is the number 60 divisible by 4?

Divisibility Rules for 4

To find out if a certain number is divisible by $4$ we will teach you $2$ ways to do it:

Divisibility by 4 (First Method)

A number is divisible by 4 if its last two digits are divisible by 4.

Divisibility by 4, (First method) - example 1

The number $832$
The last two digits are $32$ . $32$ is divisible by $4$ , therefore, we will determine that $832$ is divisible by $4$ .

Divisibility by 4, (First method) - example 2
The number $56712$
The last two digits are $12$ . $12$ is divisible by $4$ , therefore, we can determine that $56712$ is as well.

Divisibility by 4, (First method) - example 3
The number $415$
The last two digits are $15$ . $15$ is not divisible by $4$ , therefore, we will determine that $415$ is not either.

Do you know what the answer is?

Question 1

Is the number 16 divisible by 4?

Question 2

Is the number 16 divisible by 2?

Question 3

Is the number 61 divisible by 10?

Divisibility by 4 (Second method)

Multiply the tens digit by 2 and add the units digit. If the result is a multiple of 4, the original number is also.

Divisibility by, (Second method) - example 1
The number $832$
Let's multiply the tens digit $3$ by $2$ and add the units digit $2$ :
$3\times 2+2=8$
$8$ is divisible by $4$ , therefore, we will determine that $832$ is as well.

Divisibility by, (Second method) - example 2
The number $56712$
Let's multiply the tens digit $1$ by $2$ and add the units digit $2$ :
$1\times 2+2=4$
$4$ is divisible by $4$ , therefore, we will determine that $56712$ is also $4$ .

Divisibility by, (Second method) - example 3
The number $415$
Let's multiply the tens digit $1$ by $2$ and add the units digit $5$ :
$1\times 2+5=7$
$7$ is not divisible by $4$ therefore, we will determine that $415$ is not either.

Divisibility Rules for 10

A number is divisible by $10$ if its units digit is $0$ .
Divisibility by 10 - example 1
Is the number $480$ divisible by $10$ ?
The units digit is $0$ therefore, we can determine that $480$ is divisible by $10$ .

Divisibility by 10 - example 2
Is the number $567$ divisible by $10$ ?
The units digit is $7$ and not $0$ . Consequently, the number $567$ is not divisible by $10$ .

Divisibility by 10 - example 3
Is the number $65860$ divisible by $10$ ?
The units digit is $0$ , therefore, we can determine that the number $65860$ is divisible by $10$ .

Check your understanding

Question 1

Is the number 21 divisible by 4?

Question 2

Is the number 8 divisible by 2?

Question 3

Is the number 30 divisible by 10?

Word Problem to Summarize What Was Learned

In third grade $A$ there are $4$ students, in third grade $B$ there are $2$ students, and in third grade $C$ there are $10$ students.
If we have $120$ balloons, in which grade could the balloons be distributed equally, without any remainder?

Answer: in all grades.

Solution:
Let's see if the number $120$ is divisible by $4$ .
Take the last pair of digits $20$ . $20$ is divisible by $4$ , therefore, $120$ is divisible by $4$ .
Let's see if the number $120$ is divisible by $2$ .
The units digit is $0$ even, therefore, $120$ is divisible by $2$ .
Let's see if the number $120$ is divisible by $10$ .
The units digit is $0$ , therefore, the number is divisible by $10$ .

Examples and exercises with solutions for divisibility rules for 2, 4, and 10

Exercise #1

If a number is divisible by 10, is it also therefore divisible by 2?

Video Solution

Step-by-Step Solution

The answer is yes - every number that is divisible by 10 is divisible by 2.

This can be learned through the divisibility rules of each number.

We know that to identify a number divisible by 10, we need to examine its ones digit,

only numbers whose ones digit is 0 are divisible by 10,

for example: 30, 510, 15610

We know that numbers whose ones digit is 0 are actually even numbers,

and even numbers are divisible by 2 without a remainder.

Therefore, we can be certain - every number that is divisible by 10 is also divisible by 2.

It's important to understand that this is not necessarily true in reverse, not every number that is divisible by 2 is also divisible by 10!

Answer

Yes.

Exercise #2

The number 21...

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Check if 21 is divisible by 2.
Step 2: Check if 21 is divisible by 4.
Step 3: Check if 21 is divisible by 10.

Now, let's work through each step:

Step 1: A number is divisible by 2 if it is even. The number 21 ends in 1, which is odd, so 21 is not divisible by 2.

Step 2: A number is divisible by 4 if the number formed by its last two digits is divisible by 4. The number 21 is less than 40, and 21 divided by 4 gives a remainder, so 21 is not divisible by 4.

Step 3: A number is divisible by 10 if it ends in 0. The number 21 ends in 1, so it is not divisible by 10.

After evaluating all the options, we find that 21 does not meet any of the divisibility conditions given. Therefore, the solution to the problem is that 21 does not divide by any of the options.

Answer

...does not divide by any of the options.

Exercise #3

The number 301...

Step-by-Step Solution

To solve this problem, we'll apply divisibility rules to the number 301:

Divisibility by 2:
A number is divisible by 2 if its last digit is even. Since the last digit of 301 is 1, which is not even, 301 is not divisible by 2.
Divisibility by 4:
A number is divisible by 4 if the last two digits form a number divisible by 4. The last two digits of 301 are 01, which is 1. Since 1 is not divisible by 4, 301 is not divisible by 4.
Divisibility by 10:
A number is divisible by 10 if its last digit is 0. The last digit of 301 is 1, not 0, so 301 is not divisible by 10.

None of the divisibility rules for 2, 4, or 10 are satisfied by the number 301. Therefore, the correct answer is No answer is correct, corresponding to choice 4.

Answer

No answer is correct.

Exercise #4

The number 100...

Step-by-Step Solution

To solve this problem, we'll evaluate the divisibility of 100 by 2, 4, and 10:

Check divisibility by 2: A number is divisible by 2 if it is an even number. Since 100 ends in 0 (an even digit), it is divisible by 2.
Check divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4. The last two digits are 00, and $00 \div 4 = 0$ , which is divisible. Hence, 100 is divisible by 4.
Check divisibility by 10: A number is divisible by 10 if its last digit is 0. Since the last digit of 100 is 0, it is divisible by 10.

Based on these checks, all conditions for divisibility are satisfied. Therefore, the correct choice is that all answers are correct.

All answers are correct.

Answer

All answers are correct.

Exercise #5

The number 32...

Step-by-Step Solution

To determine the divisibility of 32, we'll use divisibility rules:

Step 1: Divisibility by 2
A number is divisible by 2 if its last digit is even. The last digit of 32 is 2, which is even. Therefore, 32 is divisible by 2.
Step 2: Divisibility by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Here, the number formed by the last two digits is 32. Since $32 \div 4 = 8$ , which is an integer, 32 is divisible by 4.
Step 3: Divisibility by 10
A number is divisible by 10 if its last digit is 0. The last digit of 32 is 2, not 0. Therefore, 32 is not divisible by 10.

Considering the choices provided, the correct statement is that 32 is divisible by both 2 and 4 but not by 10.

Therefore, the solution to the problem is ...is divisible by 2 and also by 4.

Answer

...is divisible by 2 and also by 4.

Do you think you will be able to solve it?

Question 1

Is the number 42 divisible by 2?

Question 2

Is the number 43 divisible by 4?

Question 3

Choose the correct answer

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Divisibility Rules for 2, 4, and 10

Divisibility Rules for 2, 4, and 10

Divisibility Criteria for 2

Divisibility Rules for 4

Divisibility Rules for 10

Test yourself on divisibility rules for 2, 4 and 10!

Divisibility Rules for 2, 4, and 10

Divisibility Rules for 2

Divisibility Rules for 4

Divisibility by 4 (First Method)

A number is divisible by 4 if its last two digits are divisible by 4.

Divisibility by 4 (Second method)

Divisibility Rules for 10

Word Problem to Summarize What Was Learned

Examples and exercises with solutions for divisibility rules for 2, 4, and 10

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Step-by-Step Solution

Answer

Exercise #3

Step-by-Step Solution

Answer

Exercise #4

Step-by-Step Solution

Answer

Exercise #5

Step-by-Step Solution

Answer

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Divisibility Rules for 2, 4 and 10