How to find out if a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 etc? Divisibility Rules

Here is an easy way to learn weather a given number is divisible by another. Traditional division method will take too much time for big numbers but if you know this divisibility rules and tricks than it will be much easier and on a test, no chance of getting wrong.This rules will defiantly help you doing fast and effective calculation(Mental Math) in the future.

1) Divisibility rule for number 1:

Every number is divisible by 1

Example: Is 5 divisible by 1? YES

2) Divisibility rule for number 2:

The last digit of the given number should be even. That means the number should end in 0, 2, 4, 6 and 8.

Example: Is 1875494  divisible by 2?

Last digit is 4 and it is even number so this  fat number 1875494 is divisible by 2. No need of doing big Division:) pretty easy huh..

3) Divisibility rule for number 3:

Add up all the digits and it should be multiple of 3 (divisible by 3)

Example: Is 2742204 divisible by 3?

Add up all the digits that is 2+7+3+4+2+2+0+4=24. 24 is divisible by  (8×3)/3 so this number 2742204 is divisible by 3 as well.

4) Divisibility rule for number 4:

The last 2 digit (ones and tens) should be divisible by 4

Example: Is 8763424 divisible by 4?

Check the last 2 digits, that is 24 and 24 is divisible by  (4×6) /3  so this big number 8763424 is divisible by 4.

5) Divisibility rule for number 5:

The last digit should be 0 or 5

Example: Is 498730 divisible by 5?

The last digit is 0 so this number 498730 is divisible by 5

Example: Is 285 divisible by 5?

The last digit is 5 so 285 is divisible by 5. Very very easy to remember, isn’t it?

6) Divisibility rule for number 6:

The rule for checking whether a number is divisible by 6 is quite tricky.

Since 6=2×3

We must apply the rules of 2 and 3 on a number to check if it is divisible by 6. So rules are

1) The last digit should be even number ( Divisibility trick for 2)

2) Add up all the digits and it should be multiple of 3 (divisible by 3)

Example:  Is 2742204 divisible by 6?

The last digit in 2742204 is 4 and it is even number. Add up all the digits so 2+7+3+4+2+2+0+4=24. 24 is divisible by 3 . this number 2742204 satisfy both the rules (2 &3) so it is divisible by 6.

7)  Divisibility rule for number 7:

There are 2 methods to check weather a given number is divisible by 7.

1) This method is good for 3 or 4 digit number:

Method: 1) Double the last digit

2) Subtract (Minus) it from the remaining digits

3) The answer should be divisible by 7 . Let’s check the example:

Example: Is 434 divisible by 7?

The last digit is 4 so double it (4×2=8). Now subtract 8 from remaining number 43,  43-8=35 and 35 is divisible by 7 (7×5=35). So 434 is also divisible by 7.

2) This method is good for more than 5 digit number( This is the rule for 7) :

Method:  1) Take beginning of the number from right and multiply it by 1, 3, 2, 6, 4, 5 sequence. Remember this sequence

otherwise your answer will be wrong . If you still don’t understand, then check the example.

2)  For 7 or more digits number, repeat this sequence.

3) Add up all. If the sum(total) is divisible by 7 than that big fat number is divisible by 7 as well.

Example: Is 373212 divisible by 7?

2(1)+7(3)+3(2)+2(6)+1(4)+2(5) = 2+21+6+12+4+10 = 56 and 56 is  divisible by 7 so this number 373212 is divisible by 7 as well.

8)  Divisibility rule for number 8:

Method-1:

1) The last 3 digits should be divisible by 8.

2)  A number with three zeros in last 3 digits are always divisible by 8.

Example: Is 3587008 divisible by 8?

Check: the last 3 digits are 008 that means 8 and 8 is divisible by 8 (8×1=8) so 3587008 is divisible  by 8.

Example  Is 90,000  divisible by 8?

Check: the last 3 digits are 0′s so 90,000 is divisible by 8.

CONFUSION?

8=4×2 so if a number follows the divisibility rules of 4 and 2, then the number is divisible by 8? It is not always true Let’s see how…

1) The last digit should be even number ( Divisibility trick for 2)

2) The last 2 digit (ones and tens) should be divisible by 4.

Example: Is 924 divisible by 8?

Check: 1) the last digit is 4 and it is even number.

2) The last 2 digits are 24 and it is divisible by 4 (4×6=24) so this number 924 should be divisible by 8 but it is not while the number 384 follows this rule so now a days we don’t follow 8=4×2 rules.

9)  Divisibility rule for number 9:

Method: 9=3×3 so it will follow divisibility rule of 3

Add up all the digits and it should be multiple of 9 (divisible by 9)

Example: Is 2742204 divisible by 9?

Add up all the digits that is 2+7+3+4+2+2+0+4=24. 24 is divisible by 9 so this number 2742204 is not divisible by 9.

Example: Is 2742234 divisible by 9?

Add up all the digits: 2+7+3+4+2+2+3+4=27 and 27 is divisible by 9 (9×3=27) so this big fat number 2742234 is divisible by 9.

10)  Divisibility rule for number 10:

Mehtod: The last digit should be 0(Multiples of 10)

Example: Is 900 divisible by 10?

Check:       Yes because the last digit is 0

11)  Divisibility rule for number 11:

Method: 1)  Add up every second digit

2) Subtract rest of the digits and answer should be 0 or divisible by 11. Check the example.

Example: Is 254987 divisible by 11?

Check:  Add up every 2nd digit: (5+9+7) – (2+4+8) = 21-14=7 .  The answer is not 0 or a multiple of 11 so this number 254987 is not divisible by 11.

Example: Is 558987 divisible by 11?

Check: (5+9+7) – (5+8+8) = 21- 21=0  Answer is 0 so 558987 is divisible by 11.

12)  Divisibility rule for number 12:

Method: 12=3×4 so if the number follows the divisibility rules of 3 and 4 is divisible by 12.

1) Add up all the digits and it should be multiple of 3 (divisible by 3)

2) The last 2 digit (ones and tens) should be divisible by 4

Example: Is 834864 divisible by 12?

Check; add up all the digits: 8+3+4+8+6+4=33 and it is multiple of  (3×11)/3

The last two digits are 64 and it is divisible by  (4×16)/3  so this number 834864 is divisible by 12.

13) Divisibility rule for number 13:

This rules are too complicated to understand so it is better to do it with our traditional division method. In case any of you are interested then, just remove the last digit and multiply it (that last digit) with 4 and add to the remaining digits. Do this sequence until only 2 digits remain and those 2 digits should be divisible by 13.

Example  Is 1543 divisible by 13?

Check: 1) Remove the last digit 3 and multiply it by 4 and add to rest of the digit so 3×4=12; 154+12=166

2) Again remove 6 and multiply by 4 and add to rest of the digit so 6×4=24 ; 16+24=40

40 is not divisible by 13 so 1543 is not divisible by 13.

14) Divisibility rule for number 14:

Method: 14=2×7 so number should be divisible by 2 as well as 7 so apply divisibility rules of 2 and 7

15) Divisibility rule for number 15:

Method: 15=3×5 so number should be divisible by 3 as well as 5. Apply divisibility rule of 3 and 5.

16) Divisibility rule for number 16:

Method:  Again it is very complicated, you must have to divide the last 4 digits by 16. and if it is divisible by 16 then any given big number is divisible by 16.

Example: Is 976347648 divisible by 16?

Check: Take the last four digits. 7648 and divide it by 16. answer is 478 so it is divisible by 16 so you can say that this 9 digits number 976347648 is divisible by 16 as well.

17) Divisibility rule for number 17:

Method: 1) Multiply the last digit by 5

2) Subtract it from the rest and if the answer is divisible by 17 then that number is divisible by 17 as well.

Example: Is 765 divisible by 17?

Check:  1) Multiply the last digit by 5 that is 5×5=25

2)  Subtract it from the rest that is 76-25=51 and 51 is divisible by ( 17×3=51)/3  so 765 is divisible by 17 as well.

18) Divisibility rule for number 18:

18=2×9 so apply divisibility rule of number 2 and 9.

19) Divisibility rule for number 19:

Method: 1) Double the last digit.

2) Add to the rest of the numbers until you get two or three digit number that  should be divisible by 19.

Example: Is 6688 divisible by 19?

Check;  8×2=16, Add 16 to the rest of the number so 668+16=684

Repeat it again: 4×2=8 and add to 68+8=76 and 76 is divisible by 19 so this number 6688 is divisible by 19 as well.

20) Divisibility rule for number 20:

Method: 1) The last digit should be 0 ( divisible by 10)

2) The second last digit should be even.

Example: Is 4490 divisible by 20?

Check:  The last digit is 0 but the last 2nd digit 9 is not even number so 4490 is not divisible by 20.

Method-2:  The last 2 digits should be divisible by 20

Example: Is 654880 divisible by 20?

Check: The last 2 digits are 80 and it is divisible by 20 (20×4=80) so 654880 is divisible by 20 as well.

 

Note: For 2nd to 7th grade  LEARN 1 to 11 divisibility rules and if you are in the advance math learn the rest.

Okay so I hope you liked all of this. So don’t get scared when you see all these ‘big fat’ numbers!

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we are school going kids and love to share our knowledge. Sometimes we get tired of browsing library catalog, Google and Wikipedia for certain information so we thought why don't we share our hard work with you ??:) We hope you will enjoy our work!

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  1. thank you so much!

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  1. [...] that we have learned as a beginner but here is short cuts methods involved in the Addition.Our Divisibility rules for 1 to 20 is big hit, now it is turn to learn quick addition method. You should teach your elementary child [...]

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