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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 66 example ( Enter your problem )
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65. Divisibility rule of 65 example
(Previous example)		67. Divisibility rule of 67 example
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66. Divisibility rule of 66 example


1. Check whether 17688 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 17688 is 8, which is divisible by 2.

`:.` 17688 is divisible by 2.


Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 17688 is `1+7+6+8+8=30`, which is divisible by 3.


`:.` 17688 is divisible by 3.


Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)

`1768color{red}{8}=>1768 - color{red}{8} = 1760`

`176color{red}{0}=>176 - color{red}{0} = 176`

`17color{red}{6}=>17 - color{red}{6} = 11`

Here 11 is divisible by 11.
`:.` 17688 is divisible by 11.

Method-2 :
Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.

Sum of digits in odd positions : `1+6+8=15`

Sum of digits in even positions : `7+8=15`

Difference `=15-15=0`

which is divisible by 11.

`:.` 17688 is divisible by 11.


17688 is divisible by 2,3 and 11.

`:.` 17688 is divisible by 66.


2. Check whether 20196 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 20196 is 6, which is divisible by 2.

`:.` 20196 is divisible by 2.


Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 20196 is `2+0+1+9+6=18`, which is divisible by 3.


`:.` 20196 is divisible by 3.


Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)

`2019color{red}{6}=>2019 - color{red}{6} = 2013`

`201color{red}{3}=>201 - color{red}{3} = 198`

`19color{red}{8}=>19 - color{red}{8} = 11`

Here 11 is divisible by 11.
`:.` 20196 is divisible by 11.

Method-2 :
Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.

Sum of digits in odd positions : `2+1+6=9`

Sum of digits in even positions : `0+9=9`

Difference `=9-9=0`

which is divisible by 11.

`:.` 20196 is divisible by 11.


20196 is divisible by 2,3 and 11.

`:.` 20196 is divisible by 66.


3. Check whether 24816 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 24816 is 6, which is divisible by 2.

`:.` 24816 is divisible by 2.


Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 24816 is `2+4+8+1+6=21`, which is divisible by 3.


`:.` 24816 is divisible by 3.


Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)

`2481color{red}{6}=>2481 - color{red}{6} = 2475`

`247color{red}{5}=>247 - color{red}{5} = 242`

`24color{red}{2}=>24 - color{red}{2} = 22`

Here 22 is divisible by 11.
`:.` 24816 is divisible by 11.

Method-2 :
Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.

Sum of digits in odd positions : `2+8+6=16`

Sum of digits in even positions : `4+1=5`

Difference `=5-16=-11`

which is divisible by 11.

`:.` 24816 is divisible by 11.


24816 is divisible by 2,3 and 11.

`:.` 24816 is divisible by 66.


4. Check whether 17629 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 17629 is 9, which is not divisible by 2.

`:.` 17629 is not divisible by 2.


Hence 17629 is also not divisible by 66.

5. Check whether 22552 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 22552 is 2, which is divisible by 2.

`:.` 22552 is divisible by 2.


Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 22552 is `2+2+5+5+2=16`, which is not divisible by 3.


`:.` 22552 is not divisible by 3.


Hence 22552 is also not divisible by 66.

6. Check whether 24390 is divisible by 66 or not?

Solution:
Divisibility rule of 66 :
If number is divisible by 2,3 and 11, then number is also divisible by 66.

Divisibility rule of 2 :
The last digit is even, then number is divisible by 2.

Last digit of 24390 is 0, which is divisible by 2.

`:.` 24390 is divisible by 2.


Divisibility rule of 3 :
The sum of the digits is divisible by 3, then number is also divisible by 3.

Sum of digits of 24390 is `2+4+3+9+0=18`, which is divisible by 3.


`:.` 24390 is divisible by 3.


Divisibility rule of 11 :
Subtract the last digit from the rest of the number.
If the answer is divisible by 11, then number is also divisible by 11.
(Apply this rule to the answer again if necessary)

`2439color{red}{0}=>2439 - color{red}{0} = 2439`

`243color{red}{9}=>243 - color{red}{9} = 234`

`23color{red}{4}=>23 - color{red}{4} = 19`

Here 19 is not divisible by 11.
`:.` 24390 is not divisible by 11.

Method-2 :
Divisibility rule of 11 :
(Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11, then number is also divisible by 11.

Sum of digits in odd positions : `2+3+0=5`

Sum of digits in even positions : `4+9=13`

Difference `=13-5=8`

which is not divisible by 11.

`:.` 24390 is not divisible by 11.


Hence 24390 is also not divisible by 66.



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