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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 69 example ( Enter your problem )
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68. Divisibility rule of 68 example
(Previous example)		70. Divisibility rule of 70 example
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69. Divisibility rule of 69 example


1. Check whether 18216 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`1821color{red}{6}=>1821 + color{red}{6} xx 7 = 1821 +42 = 1863`

`186color{red}{3}=>186 + color{red}{3} xx 7 = 186 +21 = 207`

`20color{red}{7}=>20 + color{red}{7} xx 7 = 20 +49 = 69`

Here 69 is divisible by 69.
`:.` 18216 is divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 18216 is `1+8+2+1+6=18`, which is divisible by 3.


`:.` 18216 is divisible by 3.


Divisibility rule of 23 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)

`1821color{red}{6}=>1821 + color{red}{6} xx 7 = 1821 +42 = 1863`

`186color{red}{3}=>186 + color{red}{3} xx 7 = 186 +21 = 207`

`20color{red}{7}=>20 + color{red}{7} xx 7 = 20 +49 = 69`

Here 69 is divisible by 23.
`:.` 18216 is divisible by 23.


18216 is divisible by 3 and 23.

`:.` 18216 is divisible by 69.


2. Check whether 21390 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`2139color{red}{0}=>2139 + color{red}{0} xx 7 = 2139 = 2139`

`213color{red}{9}=>213 + color{red}{9} xx 7 = 213 +63 = 276`

`27color{red}{6}=>27 + color{red}{6} xx 7 = 27 +42 = 69`

Here 69 is divisible by 69.
`:.` 21390 is divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 21390 is `2+1+3+9+0=15`, which is divisible by 3.


`:.` 21390 is divisible by 3.


Divisibility rule of 23 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)

`2139color{red}{0}=>2139 + color{red}{0} xx 7 = 2139 = 2139`

`213color{red}{9}=>213 + color{red}{9} xx 7 = 213 +63 = 276`

`27color{red}{6}=>27 + color{red}{6} xx 7 = 27 +42 = 69`

Here 69 is divisible by 23.
`:.` 21390 is divisible by 23.


21390 is divisible by 3 and 23.

`:.` 21390 is divisible by 69.


3. Check whether 27048 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`2704color{red}{8}=>2704 + color{red}{8} xx 7 = 2704 +56 = 2760`

`276color{red}{0}=>276 + color{red}{0} xx 7 = 276 = 276`

`27color{red}{6}=>27 + color{red}{6} xx 7 = 27 +42 = 69`

Here 69 is divisible by 69.
`:.` 27048 is divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 27048 is `2+7+0+4+8=21`, which is divisible by 3.


`:.` 27048 is divisible by 3.


Divisibility rule of 23 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)

`2704color{red}{8}=>2704 + color{red}{8} xx 7 = 2704 +56 = 2760`

`276color{red}{0}=>276 + color{red}{0} xx 7 = 276 = 276`

`27color{red}{6}=>27 + color{red}{6} xx 7 = 27 +42 = 69`

Here 69 is divisible by 23.
`:.` 27048 is divisible by 23.


27048 is divisible by 3 and 23.

`:.` 27048 is divisible by 69.


4. Check whether 19201 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`1920color{red}{1}=>1920 + color{red}{1} xx 7 = 1920 +7 = 1927`

`192color{red}{7}=>192 + color{red}{7} xx 7 = 192 +49 = 241`

`24color{red}{1}=>24 + color{red}{1} xx 7 = 24 +7 = 31`

Here 31 is not divisible by 69.
`:.` 19201 is not divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 19201 is `1+9+2+0+1=13`, which is not divisible by 3.


`:.` 19201 is not divisible by 3.


Hence 19201 is also not divisible by 69.

5. Check whether 21168 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`2116color{red}{8}=>2116 + color{red}{8} xx 7 = 2116 +56 = 2172`

`217color{red}{2}=>217 + color{red}{2} xx 7 = 217 +14 = 231`

`23color{red}{1}=>23 + color{red}{1} xx 7 = 23 +7 = 30`

Here 30 is not divisible by 69.
`:.` 21168 is not divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 21168 is `2+1+1+6+8=18`, which is divisible by 3.


`:.` 21168 is divisible by 3.


Divisibility rule of 23 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 23, then number is also divisible by 23.
(Apply this rule to the answer again if necessary)

`2116color{red}{8}=>2116 + color{red}{8} xx 7 = 2116 +56 = 2172`

`217color{red}{2}=>217 + color{red}{2} xx 7 = 217 +14 = 231`

`23color{red}{1}=>23 + color{red}{1} xx 7 = 23 +7 = 30`

Here 30 is not divisible by 23.
`:.` 21168 is not divisible by 23.


Hence 21168 is also not divisible by 69.

6. Check whether 26636 is divisible by 69 or not?

Solution:
Divisibility rule of 69 :
7 times the last digit and add it to the rest of the number.
If the answer is divisible by 69, then number is also divisible by 69.
(Apply this rule to the answer again if necessary)

`2663color{red}{6}=>2663 + color{red}{6} xx 7 = 2663 +42 = 2705`

`270color{red}{5}=>270 + color{red}{5} xx 7 = 270 +35 = 305`

`30color{red}{5}=>30 + color{red}{5} xx 7 = 30 +35 = 65`

Here 65 is not divisible by 69.
`:.` 26636 is not divisible by 69.

Method-2 :
Divisibility rule of 69 :
If number is divisible by 3 and 23, then number is also divisible by 69.

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

Sum of digits of 26636 is `2+6+6+3+6=23`, which is not divisible by 3.


`:.` 26636 is not divisible by 3.


Hence 26636 is also not divisible by 69.



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