# Divisibility rules from 14 to 30 with examples

Divisibility rules(14 to 30) which are used to check the divisibility of a given number without calculation especially division. We can say it is the   shorthand method for division. In this Content we will come to know about the Divisibility rules from 14 to 30 with examples.

## Divisibility rules for 14:–

A number is divisible by 14, if the number is divisible by 2 and by 7.

Example- 294

•        294 is divisible 2 because its last digit is 4.
•        294 is divisible by 7 as (two times of last digit is 8.and 29-8=21 which is divisible by 7).

Hence 294 is divisible by 14.

## Divisibility rules for 15:-

A number is divisible by 15, if the number is divisible by 3 and by 5.

Example: – Check 720 is divisible by 15 or not?

·        First check 720 is divisible by 3 or not. According to the divisibility rule by 3(sum of its digit=7+2+0=9, which is divisible by 3), 720 is divisible by 3.

·        And now check 720 is divisible by 5 or not.

Divisibility rule 5- if unit digit of the number is either 0 or 5, then number is divisible by 5.Here 720 is the given number and unit digit is 0.So 720 is divisible by 5.

720 is divisible by both 3 and 5.Hence 720 is divisible by 15.

## Divisibility rules for 16:–

Add last two digit of a number to the four times of the rest of that given number. The result must be divisible by 16.

Example: – Check 1008 is divisible by 16 or not?

·       Last two digit 0 and 8.

·       Four times of the rest of the number. i.e. =10*4=40.

·       Add 08 and 40.i.e. =40+8=48.That is divisible by 16.

Hence, 1008 is divisible by 16.

## Divisibility Rules for 17:

Subtract five times of the unit digit from remaining number, if the result is 0

or divisible by 17 then the number is divisible by 17.

Example- check 357 is divisible by 17 or not.

·       Calculate five times of the unit digit of given number i.e. 7*5=35.

·       Subtract above multiplication value from remaining number.i.e.35-35=0

·       If result is 0 or divisible by 17 then the given number is divisible by 17. Here ‘0’ came as result. Hence, 357 is divisible by 17.

## Divisibility Rules for 18:-

A number is divisible by 18, if the number is divisible by 2 and by 9.

Example- check 576 whether it is divisible by 18 or not?

According to the divisibility rules a number is divisible by 18 if that number is divisible by 2 and by 9.

576 is divisible by 2 as its last/unit digit is 0, 2,4,6,8.

576 is divisible by 9 as its sum of digits is=5+7+6=18.

Which is divisible by 9.

## Divisibility Rules for 19:

Add two times the unit/last digit of the number to the rest of the number and if the result is divisible by 19 then the given number is divisible by 19.

Example: – check 437 is divisible by 19 or not?

§  Last digit of the number is =7

§  Double  the last digit means 7*2=14

§  Now add 14 to the rest of the number 43. Result=43+14=57.

§  Which is divisible by 19.

## Divisibility Rules for 20:

A number is divisible by 20 if it is divisible by 10 and its tens digit is even.

Example: – check 564720 is divisible by 20 or not?

·       564720 is divisible by 10 as its unit digit is 0.

·       And its tens digit is even (2).

Hence 564720 is divisible by 20.

## Divisibility Rules for 21:

A number is divisible by 21 if it is divisible by 3 and by 7.

Example: -check 1365 .it is divisible by 21 or not.

·       1365 is divisible by 3 as its sum of digits =1+3+6+5=15(that is divisible by 3)

·       1365 is also divisible by 7.

·       According to the rules of divisibility of 7.

·       Subtract two times of unit digit from the rest of the numbers.

·       Two times of unit digit is =5*2=10.

·       Rest of the number =136.

·       Subtract 136-10=126.which is divisible by 7.

Hence 1365 is divisible by 21.

Divisibility Rules for 22:

A Number is divisible by 22 if it is divisible by 2 and by 11.

Example: -Test 264 is divisible by 22 or not.

• ·      264 is divisible by 2 as its unit digit is 4.
• ·      264 is also divisible by 11 as its difference of sum of odd places digits and sum of even places digits is 0.
• ·       I.e. 2+4=6(sum of odd places digits).
• ·       And 6 is at even place.
• ·       Difference=6-6=0.

Hence 264 is divisible by 22.

## Divisibility Rules for 23:

Add 7 times of the unit digit to the rest of the number of a given number and if the result is divisible by 23 then the given number is divisible by 23.

Example: – Check 276 is divisible by 23 or not?

·       7 times of the unit digit is 7*6=42.

·       Add 42 to the rest of the number. 42+27=69.

·       69 is divisible by 23.So, the given number 276 is divisible by 23.

## Divisibility Rules for 24:

A number is divisible by 24 if it is divisible by 3 and by 8.

example-check 696 .its divisibility by 24.

·       696 is s divisible by 3 as its sum of the digits is =6+9+6=21.which is divisible by 3.

·       696 is divisible by 8.follow the steps to check

·       Add the last digit to the two times of the rest of the number.

·       69*2=138.

·       138+6=144.

·       take one more step to check the divisibility

·       14*2=28+4=32.which is divisible by 8.

Hence 696 is divisible by 24.

## Divisibility Rules for 25:

A number is divisible by 25 if its last two digits are 00,25,50,75.

Example – check 52625 is divisible by 25 or not.

According to the rule, last two digits in given number is 25.

Hence 52625 is divisible by 25.

## Divisibility Rules for 26 :

A number is divisible by 26 if the number is divisible by 2 and by 13.

Example:-

Check 2548 is divisible by 26 or not.

First check it is divisible by 2 or not.

It is divisible by 2 as its unit digit is 8.

Now check with 13.

Calculate four times of the unit digit.i.e.8*4=32.

Add it to the remaining number.254+32=286.

One more step to follow.

Take four times of unit digit of 286.i.e.6*4=24.

Add 28+24=52.which is divisible by 13.

Hence 2548 is divisible by 26.

## Divisibility rules for 27:–

Subtract 8 times of the unit digit from the rest of the number. If the resultant number is divisible by 27 then the given number is divisible by 27.

Example:-Check 945 .whether it is divisible by 27 or not.

·       Calculate the 8 times of the unit digit. i.e.5*8=40.

·       Subtract it from rest of the number. I.e. 94-40=54.which is divisible by 27.

Hence 945 is divisible by 27.

Divisibility rules for 28:-

A number is divisible by 28 if it is divisible by 4 and by 7.

Example: – Check divisibility of 252 by 28.

·       First check with 4.According to Divisibility rule for 4, the number formed by last two digit must be divisible by 4.

·       Here number formed by last two digit is 52.Which is divisible by 4.

·       Now check with 7.For that calculate the double of the unit digit .I.e.2*2=4.

·       Now subtract it from the rest of the number.25-4=21.which is divisible by 7.

Hence 252 is divisible by 28.

## Divisibility Rules for 29:

Add 3 times of the unit digit to the rest of the number of a given number and if the result is divisible by 29 then the given number is divisible by 29.

Example: – Check 435 is divisible by 29 or not?

·       3 times of the unit digit is =3*5=15.

·       Add 15 to the rest of the number = 43+15=58.

·       58 is divisible by 29. So, the number is divisible by 29.

## Divisibility Rules for 30:

A number is divisible by 30 if it is divisible by 3 and by 10.

Example: – Test 5320 is divisible by 30 or not.

·       First we will check for 3.According to divisibility rule of 3, the sum of the digits must be divisible by 3.

·       Here sum=5+3+2+0=10.which is not divisible by 3.So no need to check for 10.5320 is not going to divisible by 30.

Take one more number 450.

·       450 is divisible by 3.As its sum of digits is 4+5+0=9.which is divisible by 3.

·       450 is also divisible by 10.As its unit digit is 0.

Hence 450 is divisible by 30.

Solved Questions:

1.    12366 is divisible by

12366=2*6183

12366=6*2061

12366=18*687

12366=54*229

12366 is divisible by 2,3,6,9,18,54,6183,2061,687,229.

Divisibility rules in math