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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 42 example ( Enter your problem )
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41. Divisibility rule of 41 example
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42. Divisibility rule of 42 example


1. Check whether 12096 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 12096 is 6, which is divisible by 2.

`:.` 12096 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 12096 is `1+2+0+9+6=18`, which is divisible by 3.


`:.` 12096 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)

`1209color{red}{6}=>1209 - color{red}{6} xx 2 = 1209 -12 = 1197`

`119color{red}{7}=>119 - color{red}{7} xx 2 = 119 -14 = 105`

`10color{red}{5}=>10 - color{red}{5} xx 2 = 10 -10 = 0`

Here 0 is divisible by 7.
`:.` 12096 is divisible by 7.


12096 is divisible by 2,3 and 7.

`:.` 12096 is divisible by 42.


2. Check whether 13314 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 13314 is 4, which is divisible by 2.

`:.` 13314 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 13314 is `1+3+3+1+4=12`, which is divisible by 3.


`:.` 13314 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)

`1331color{red}{4}=>1331 - color{red}{4} xx 2 = 1331 -8 = 1323`

`132color{red}{3}=>132 - color{red}{3} xx 2 = 132 -6 = 126`

`12color{red}{6}=>12 - color{red}{6} xx 2 = 12 -12 = 0`

Here 0 is divisible by 7.
`:.` 13314 is divisible by 7.


13314 is divisible by 2,3 and 7.

`:.` 13314 is divisible by 42.


3. Check whether 15834 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 15834 is 4, which is divisible by 2.

`:.` 15834 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 15834 is `1+5+8+3+4=21`, which is divisible by 3.


`:.` 15834 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)

`1583color{red}{4}=>1583 - color{red}{4} xx 2 = 1583 -8 = 1575`

`157color{red}{5}=>157 - color{red}{5} xx 2 = 157 -10 = 147`

`14color{red}{7}=>14 - color{red}{7} xx 2 = 14 -14 = 0`

Here 0 is divisible by 7.
`:.` 15834 is divisible by 7.


15834 is divisible by 2,3 and 7.

`:.` 15834 is divisible by 42.


4. Check whether 10880 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 10880 is 0, which is divisible by 2.

`:.` 10880 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 10880 is `1+0+8+8+0=17`, which is not divisible by 3.


`:.` 10880 is not divisible by 3.


Hence 10880 is also not divisible by 42.

5. Check whether 14044 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 14044 is 4, which is divisible by 2.

`:.` 14044 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 14044 is `1+4+0+4+4=13`, which is not divisible by 3.


`:.` 14044 is not divisible by 3.


Hence 14044 is also not divisible by 42.

6. Check whether 15381 is divisible by 42 or not?

Solution:
Divisibility rule of 42 :
If number is divisible by 2,3 and 7, then number is also divisible by 42.

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

Last digit of 15381 is 1, which is not divisible by 2.

`:.` 15381 is not divisible by 2.


Hence 15381 is also not divisible by 42.


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