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Home > Pre-Algebra calculators > Divisibility rule example
Divisibility rule of 74 example ( Enter your problem )
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73. Divisibility rule of 73 example
(Previous example)		75. Divisibility rule of 75 example
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74. Divisibility rule of 74 example


1. Check whether 21830 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 21830 is 0, which is divisible by 2.

`:.` 21830 is divisible by 2.


Divisibility rule of 37 :
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)

`2183color{red}{0}=>2183 - color{red}{0} xx 11 = 2183 = 2183`

`218color{red}{3}=>218 - color{red}{3} xx 11 = 218 -33 = 185`

`18color{red}{5}=>18 - color{red}{5} xx 11 = 18 -55 = -37`

Here -37 is divisible by 37.
`:.` 21830 is divisible by 37.


21830 is divisible by 2 and 37.

`:.` 21830 is divisible by 74.


2. Check whether 22348 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 22348 is 8, which is divisible by 2.

`:.` 22348 is divisible by 2.


Divisibility rule of 37 :
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)

`2234color{red}{8}=>2234 - color{red}{8} xx 11 = 2234 -88 = 2146`

`214color{red}{6}=>214 - color{red}{6} xx 11 = 214 -66 = 148`

`14color{red}{8}=>14 - color{red}{8} xx 11 = 14 -88 = -74`

Here -74 is divisible by 37.
`:.` 22348 is divisible by 37.


22348 is divisible by 2 and 37.

`:.` 22348 is divisible by 74.


3. Check whether 27824 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 27824 is 4, which is divisible by 2.

`:.` 27824 is divisible by 2.


Divisibility rule of 37 :
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)

`2782color{red}{4}=>2782 - color{red}{4} xx 11 = 2782 -44 = 2738`

`273color{red}{8}=>273 - color{red}{8} xx 11 = 273 -88 = 185`

`18color{red}{5}=>18 - color{red}{5} xx 11 = 18 -55 = -37`

Here -37 is divisible by 37.
`:.` 27824 is divisible by 37.


27824 is divisible by 2 and 37.

`:.` 27824 is divisible by 74.


4. Check whether 19605 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 19605 is 5, which is not divisible by 2.

`:.` 19605 is not divisible by 2.


Hence 19605 is also not divisible by 74.

5. Check whether 23006 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 23006 is 6, which is divisible by 2.

`:.` 23006 is divisible by 2.


Divisibility rule of 37 :
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)

`2300color{red}{6}=>2300 - color{red}{6} xx 11 = 2300 -66 = 2234`

`223color{red}{4}=>223 - color{red}{4} xx 11 = 223 -44 = 179`

`17color{red}{9}=>17 - color{red}{9} xx 11 = 17 -99 = -82`

Here -82 is not divisible by 37.
`:.` 23006 is not divisible by 37.


Hence 23006 is also not divisible by 74.

6. Check whether 28298 is divisible by 74 or not?

Solution:
Divisibility rule of 74 :
If number is divisible by 2 and 37, then number is also divisible by 74.

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

Last digit of 28298 is 8, which is divisible by 2.

`:.` 28298 is divisible by 2.


Divisibility rule of 37 :
11 times the last digit and subtract it from the rest of the number.
If the answer is divisible by 37, then number is also divisible by 37.
(Apply this rule to the answer again if necessary)

`2829color{red}{8}=>2829 - color{red}{8} xx 11 = 2829 -88 = 2741`

`274color{red}{1}=>274 - color{red}{1} xx 11 = 274 -11 = 263`

`26color{red}{3}=>26 - color{red}{3} xx 11 = 26 -33 = -7`

Here -7 is not divisible by 37.
`:.` 28298 is not divisible by 37.


Hence 28298 is also not divisible by 74.


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73. Divisibility rule of 73 example
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