Divisibility Rules for 2, 4, and 10

🏆Practice signs of division by 2, 4 and 10

Divisibility Rules for 2, 4, and 10

Divisibility Criteria for 2

A number is divisible by 22 if the units digit is even - that is, it divides by 22 without a remainder.

Divisibility Rules for 4

First way: A number is divisible by 44 if its last two digits are divisible by 44.
Second way: Multiply the tens digit by 22 and add the units digit. If the result obtained is a multiple of 44, then the original number is as well.

Divisibility Rules for 10

A number is divisible by 1010 if its units digit is 00.

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Test yourself on signs of division by 2, 4 and 10!

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

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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 22, by 44, and by 1010.

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Divisibility Rules for 2

A number is divisible by 22 if its units digit is even.
Let's remember that an even digit is one that can be divided by 22 without leaving a remainder.
If the units digit is odd, we can determine, without a doubt, that the number is not divisible by 22.

Divisibility by 2 - example 1
The number 4848
Let's observe the units digit 88
88 is even, therefore, we can determine that the number 4848 is divisible by 22.


Divisibility by 2 - example 2
The number 677677
Let's observe the units digit 77.
77 is odd, therefore, we can determine that 677677 is not divisible by 22.


Divisibility by 2 - example 3
Determine if the number 35783578 is divisible by 22.

Solution:
The units digit is 88, even, therefore, the number is divisible by 22.


Divisibility by 2 - example 4

Determine if the number 1000310003 is divisible by 22

Solution:
The units digit is 33, odd, therefore, the number is not divisible by 22.


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Divisibility Rules for 4

To find out if a certain number is divisible by 44 we will teach you 22 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 832832
The last two digits are 3232. 3232 is divisible by 44, therefore, we will determine that 832832 is divisible by 44.


Divisibility by 4, (First method) - example 2
The number 56712 56712
The last two digits are 1212. 1212 is divisible by 44, therefore, we can determine that 56712 56712 is as well.


Divisibility by 4, (First method) - example 3
The number 415415
The last two digits are 15151515 is not divisible by 44, therefore, we will determine that 415415 is not either.


Do you know what the answer is?

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 832832
Let's multiply the tens digit 33 by 22 and add the units digit 22:
3×2+2=83\times 2+2=8
88 is divisible by 44, therefore, we will determine that 832832 is as well.


Divisibility by, (Second method) - example 2
The number 56712 56712
Let's multiply the tens digit 11 by 22 and add the units digit 22:
1×2+2=41\times 2+2=4
44 is divisible by 44, therefore, we will determine that 56712 56712 is also 44.


Divisibility by, (Second method) - example 3
The number 415415
Let's multiply the tens digit 11 by 22 and add the units digit 55:
1×2+5=7 1\times 2+5=7
77 is not divisible by 44 therefore, we will determine that 415415 is not either.


Divisibility Rules for 10

A number is divisible by 1010 if its units digit is 00.
Divisibility by 10 - example 1
Is the number 480480 divisible by 1010?
The units digit is 00 therefore, we can determine that 480480 is divisible by 1010.


Divisibility by 10 - example 2
Is the number 567567 divisible by 1010?
The units digit is 77 and not 00. Consequently, the number 567567 is not divisible by 1010.


Divisibility by 10 - example 3
Is the number 6586065860 divisible by 1010?
The units digit is 00, therefore, we can determine that the number 6586065860 is divisible by 1010.


Check your understanding

Word Problem to Summarize What Was Learned

In third grade AA there are 44 students, in third grade BB there are 22 students, and in third grade CC there are 1010 students.
If we have 120120 balloons, in which grade could the balloons be distributed equally, without any remainder?

Answer: in all grades.

Solution:
Let's see if the number 120120 is divisible by 44.
Take the last pair of digits 2020. 2020 is divisible by 44, therefore, 120120 is divisible by 44.
Let's see if the number 120120 is divisible by 22.
The units digit is 00 even, therefore, 120120 is divisible by 22.
Let's see if the number 120120 is divisible by 1010.
The units digit is 00, therefore, the number is divisible by 1010.


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