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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 78 example ( Enter your problem )
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77. Divisibility rule of 77 example
(Previous example)		79. Divisibility rule of 79 example
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78. Divisibility rule of 78 example


1. Check whether 21372 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 21372 is 2, which is divisible by 2.

`:.` 21372 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 21372 is `2+1+3+7+2=15`, which is divisible by 3.


`:.` 21372 is divisible by 3.


Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)

`2137color{red}{2}=>2137 + color{red}{2} xx 4 = 2137 +8 = 2145`

`214color{red}{5}=>214 + color{red}{5} xx 4 = 214 +20 = 234`

`23color{red}{4}=>23 + color{red}{4} xx 4 = 23 +16 = 39`

Here 39 is divisible by 13.
`:.` 21372 is divisible by 13.


21372 is divisible by 2,3 and 13.

`:.` 21372 is divisible by 78.


2. Check whether 25194 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 25194 is 4, which is divisible by 2.

`:.` 25194 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 25194 is `2+5+1+9+4=21`, which is divisible by 3.


`:.` 25194 is divisible by 3.


Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)

`2519color{red}{4}=>2519 + color{red}{4} xx 4 = 2519 +16 = 2535`

`253color{red}{5}=>253 + color{red}{5} xx 4 = 253 +20 = 273`

`27color{red}{3}=>27 + color{red}{3} xx 4 = 27 +12 = 39`

Here 39 is divisible by 13.
`:.` 25194 is divisible by 13.


25194 is divisible by 2,3 and 13.

`:.` 25194 is divisible by 78.


3. Check whether 29250 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 29250 is 0, which is divisible by 2.

`:.` 29250 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 29250 is `2+9+2+5+0=18`, which is divisible by 3.


`:.` 29250 is divisible by 3.


Divisibility rule of 13 :
4 times the last digit and add it to the rest of the number.
If the answer is divisible by 13, then number is also divisible by 13.
(Apply this rule to the answer again if necessary)

`2925color{red}{0}=>2925 + color{red}{0} xx 4 = 2925 = 2925`

`292color{red}{5}=>292 + color{red}{5} xx 4 = 292 +20 = 312`

`31color{red}{2}=>31 + color{red}{2} xx 4 = 31 +8 = 39`

Here 39 is divisible by 13.
`:.` 29250 is divisible by 13.


29250 is divisible by 2,3 and 13.

`:.` 29250 is divisible by 78.


4. Check whether 22915 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 22915 is 5, which is not divisible by 2.

`:.` 22915 is not divisible by 2.


Hence 22915 is also not divisible by 78.

5. Check whether 25190 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 25190 is 0, which is divisible by 2.

`:.` 25190 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 25190 is `2+5+1+9+0=17`, which is not divisible by 3.


`:.` 25190 is not divisible by 3.


Hence 25190 is also not divisible by 78.

6. Check whether 30989 is divisible by 78 or not?

Solution:
Divisibility rule of 78 :
If number is divisible by 2,3 and 13, then number is also divisible by 78.

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

Last digit of 30989 is 9, which is not divisible by 2.

`:.` 30989 is not divisible by 2.


Hence 30989 is also not divisible by 78.



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