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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 21 example ( Enter your problem )
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20. Divisibility rule of 20 example
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21. Divisibility rule of 21 example


1. Check whether 5628 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`562color{red}{8}=>562 - color{red}{8} xx 2 = 562 -16 = 546`

`54color{red}{6}=>54 - color{red}{6} xx 2 = 54 -12 = 42`

Here 42 is divisible by 21.
`:.` 5628 is divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 5628 is `5+6+2+8=21`, which is divisible by 3.


`:.` 5628 is divisible by 3.


Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)

`562color{red}{8}=>562 - color{red}{8} xx 2 = 562 -16 = 546`

`54color{red}{6}=>54 - color{red}{6} xx 2 = 54 -12 = 42`

Here 42 is divisible by 7.
`:.` 5628 is divisible by 7.


5628 is divisible by 3 and 7.

`:.` 5628 is divisible by 21.


2. Check whether 6552 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`655color{red}{2}=>655 - color{red}{2} xx 2 = 655 -4 = 651`

`65color{red}{1}=>65 - color{red}{1} xx 2 = 65 -2 = 63`

Here 63 is divisible by 21.
`:.` 6552 is divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 6552 is `6+5+5+2=18`, which is divisible by 3.


`:.` 6552 is divisible by 3.


Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)

`655color{red}{2}=>655 - color{red}{2} xx 2 = 655 -4 = 651`

`65color{red}{1}=>65 - color{red}{1} xx 2 = 65 -2 = 63`

Here 63 is divisible by 7.
`:.` 6552 is divisible by 7.


6552 is divisible by 3 and 7.

`:.` 6552 is divisible by 21.


3. Check whether 7833 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`783color{red}{3}=>783 - color{red}{3} xx 2 = 783 -6 = 777`

`77color{red}{7}=>77 - color{red}{7} xx 2 = 77 -14 = 63`

Here 63 is divisible by 21.
`:.` 7833 is divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 7833 is `7+8+3+3=21`, which is divisible by 3.


`:.` 7833 is divisible by 3.


Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)

`783color{red}{3}=>783 - color{red}{3} xx 2 = 783 -6 = 777`

`77color{red}{7}=>77 - color{red}{7} xx 2 = 77 -14 = 63`

Here 63 is divisible by 7.
`:.` 7833 is divisible by 7.


7833 is divisible by 3 and 7.

`:.` 7833 is divisible by 21.


4. Check whether 5780 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`578color{red}{0}=>578 - color{red}{0} xx 2 = 578 = 578`

`57color{red}{8}=>57 - color{red}{8} xx 2 = 57 -16 = 41`

Here 41 is not divisible by 21.
`:.` 5780 is not divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 5780 is `5+7+8+0=20`, which is not divisible by 3.


`:.` 5780 is not divisible by 3.


Hence 5780 is also not divisible by 21.

5. Check whether 6627 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`662color{red}{7}=>662 - color{red}{7} xx 2 = 662 -14 = 648`

`64color{red}{8}=>64 - color{red}{8} xx 2 = 64 -16 = 48`

Here 48 is not divisible by 21.
`:.` 6627 is not divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 6627 is `6+6+2+7=21`, which is divisible by 3.


`:.` 6627 is divisible by 3.


Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)

`662color{red}{7}=>662 - color{red}{7} xx 2 = 662 -14 = 648`

`64color{red}{8}=>64 - color{red}{8} xx 2 = 64 -16 = 48`

Here 48 is not divisible by 7.
`:.` 6627 is not divisible by 7.


Hence 6627 is also not divisible by 21.

6. Check whether 7506 is divisible by 21 or not?

Solution:
Divisibility rule of 21 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 21, then number is also divisible by 21.
(Apply this rule to the answer again if necessary)

`750color{red}{6}=>750 - color{red}{6} xx 2 = 750 -12 = 738`

`73color{red}{8}=>73 - color{red}{8} xx 2 = 73 -16 = 57`

Here 57 is not divisible by 21.
`:.` 7506 is not divisible by 21.

Method-2 :
Divisibility rule of 21 :
If number is divisible by 3 and 7, then number is also divisible by 21.

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

Sum of digits of 7506 is `7+5+0+6=18`, which is divisible by 3.


`:.` 7506 is divisible by 3.


Divisibility rule of 7 :
2 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 7, then number is also divisible by 7.
(Apply this rule to the answer again if necessary)

`750color{red}{6}=>750 - color{red}{6} xx 2 = 750 -12 = 738`

`73color{red}{8}=>73 - color{red}{8} xx 2 = 73 -16 = 57`

Here 57 is not divisible by 7.
`:.` 7506 is not divisible by 7.


Hence 7506 is also not divisible by 21.



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