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# 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.**

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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. ** **

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**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**

Answer-

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.

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