Divisibility Rules for 3, 6, and 9

🏆Practice signs of division in 3, 6 and 9

Divisibility criteria for 33, 66 and 99

Divisibility criteria for 33

A number is divisible by 33 if the sum of its digits is a multiple of 33.

Divisibility criteria for 66

A number is divisible by 66 if it is even and also a multiple of 33.

Divisibility criteria for99

A number is divisible by 99 if the sum of its digits is a multiple of 99.

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Test yourself on signs of division in 3, 6 and 9!

einstein

Determine if the following number is divisible by 3:

\( 132 \)

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Divisibility Rules for 3, 6, and 9

Wow! What a pleasant and entertaining topic! In this article, we will teach you how to identify if a number is divisible by 33, 66 and 99, in a matter of seconds!
Shall we start?


Divisibility Rules for 3

A number is divisible by 33 if the sum of its digits is a multiple of 33.
If the sum of the digits of the number is not a multiple of 33, neither will the original number be.

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Test your knowledge

Example 1

The number 714714
How will we know if it is divisible by 33? In a very simple way, we will calculate the sum of its digits:
7+1+4=127+1+4=12

We already know that 1212 is divisible by 33, therefore, 714714 is as well.

Note: we recommend adding the digits one more step to avoid errors.
That is, if after adding the digits the result is 1212, we can add the new digits obtained again.
1+2=31+2=3

This sum will give us a smaller number and, in this way, we can be sure whether it is a multiple of 33 or not.
In the same way, we will know that, if the number obtained in the result is a multiple of 33, the original one is as well.


example 2

Is the number 465465 divisible by 33?
Solution: Let's check the sum of its digits:
4+6+5=154+6+5=15

1515 –> The result is, indeed, a number divisible by 33, therefore, the original 465465 is as well.
Note: We could have continued and added the digits to arrive at a smaller number.
1+5=61+5=6
66 is divisible by 33. Therefore, 465465 is also divisible by 33.


Example 3

Is the number 25472547 divisible by 33?

Solution:
2+5+4+7=182+5+4+7=18
1+8=91+8=9
99 is divisible by 33, therefore, 25472547 is divisible by 33.


Do you know what the answer is?

Example 4

Is the number 81258125 divisible by 33?

Solution:
8+1+2+5=168+1+2+5=16
1+6=71+6=7
77 is not divisible by 33, therefore, 25472547 is not divisible by 33.


Divisibility Rules for 6

A number is divisible by 66 if it is even and also a multiple of 33.
In fact, we must check the 22 conditions:

  • Let's ask if the number is even, for that we can observe the last digit and, if it is even, the whole number is.
  • Let's ask if the number is a multiple of 33. According to what we have learned, a number is divisible by 33 if the sum of its digits is a multiple of 33.

If both conditions are met, the number is divisible by 66.

Check your understanding

Example 1

Is the number 714714 divisible by 66?

Solution:
Let's see if the number is even.
Yes, the number is even. The units digit is 66 and 66 is an even number.
Let's continue with the second condition -> Is the number divisible by 33?


Example 2

Let's calculate the sum of its digits:
7+1+4=127+1+4=12
1+2=31+2=3
33 is divisible by 33, therefore, 714714 is also divisible by 33.
Both conditions are met, so 714714 is divisible by 66.

Is the number 90819081 divisible by 66?

Solution:
Let's see if the number is even:
The units digit is 11, 11 is odd, therefore, the number is not divisible by 66.
Even if only one of the conditions is not met, that is enough to determine that the number is not divisible by 66.


Do you think you will be able to solve it?

Divisibility Rules for 9

A number is divisible by 99 if the sum of its digits is a multiple of 99.
If the sum of the digits of the number is not a multiple of 99, then the original number will not be either.
Note: After adding the digits once and obtaining some number as a result, it is advisable to also add the digits of this last number to arrive at a smaller number that makes it easier to check if it is a multiple of 99.

For example

The number 864864

Solution :
Let's add its digits 8+6+4=188+6+4=18
1818 is divisible by 99 and at this stage, we can determine that 864864 is divisible by 99.
If you still doubt that 1818 is divisible by 99, you can add the digits of the result obtained again:
1+8=9 1+8=9
99 is divisible by 99, therefore, 864864 is divisible by 99.


Test your knowledge

Example 2

Is the number 81348134 divisible by 99?

Solution :
8+1+3+4=168+1+3+4=16
1+6=7 1+6=7 
77 is not divisible by 99, therefore, 81348134 is divisible by 99.


Example 3

Is the number 99459945 divisible by 99?

Solution:
9+9+4+5=279+9+4+5=27
2+7=92+7=9
99 is divisible by 99, therefore, 99459945 is divisible by 99.


Do you know what the answer is?
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