# __NUMBER SYSTEM - Part - II__

After knowing all about numbers, Divisibility is one of the most important part in Number System you have to know.

Even, if * Divisibility questions* are not asked directly, still its knowledge is very essential to solve different questions in simplification.

## Number System| Formula of Number System| Divisibility Rule| Divisibility Rule by 7| Get Number System Questions PDF with Solutions|

The knowledge of divisibility rules will help you to increase your calculation speed. That will help you to manage your time and accuracy.

### Let's discuss all about divisibility rule with Divisibility Rule by 7:

Basic Formula of Divisibility from 2 to 19

__1. Divisibility by 2:__

If the last digit of any number is 0 or an even number, then that number will be divisible by 2.

Such as, 242, 560, 678

Here all three last digit i.e. 2,0,8 are divisible by 2 so these whole numbers will be divisible by 2.

__2. Divisibility by 3:__

If the sum of all digits of any number is divisible by 3, then that number will be divisible by 3.

Such as,

432; 4+3+2=9, which is divisible by 3. So, 432 is divisible by 3.

651; 6+5+1=12, which is divisible by 3. So, 651 is divisible by 3.

__3. Divisibility by 4:__

If in any number last two digits are divisible by 4, then the whole number will be divisible by 4.

Such as,

48524, here last 2 digits i.e. 24 is divisible by 4. So, 48524 will be divisible by 4.

__4. Divisibility by 5:__

If last digit of a number is 5 or 0. Then that number is divisible by 5.

Such as, 200,225, 440 etc.

__5. Divisibility by 6:__

6= 2×3

If a number is divisible by both 2 and 3, then that number is divisible by 6 also, such as 216, 25614 etc.

You can also read : How to crack SSC CGL in first attempt without coaching

__6. Divisibility by 7:__

At first, divide numbers from left end as a group of three digits.

Then, sum and substract these groups alternatively.

Now, the result should be divisible by 7, to be divisible by 7.

Let's get an example:

3988782

Divide as a group of three digits from left end, 782, 988, 003

Now, add and substract alternatively

+782 - 988 + 003 = -203, which is divisible by 7.

__7. Divisibility by 8:__

If in any number last three digits are divisible by 8, then that whole number is divisible by 8.

Such as,

247864, here 864 is divisible by 8. So that whole number 247864 will be divisible by 8.

__8. Divisibility by 9:__

If the sum of all digits of a number is divisible by 9; then that whole number will be divisible by 9.

As, 24435. Here 2+4+4+3+5=18, which is divisible by 9. So the whole number will be divisible by 9.

__9. Divisibility by 10:__

The number whose last digit is'0'. Then that number will be divisible by 10.

Such as, 10, 200, 970 etc.

__10. Divisibility by 11:__

*1st Method:*

Alternatively add all odd position's numbers from left end, then add all even position's numbers.

Now, substract even position numbers' sum from odd position numbers' sum. This result should be "0", "11" or multiple of "11".

Let's check 123456,

Add odd position numbers -> 6+4+2 = 12

Then, add even position numbers -> 5+3+1 = 9

Now 12-9 = 3, so it's not divisible by 11.

*Another Method (Same as divisible rule by 7) :*

At first, divide numbers from left end as a group of three digits.

Then, sum and substract these groups alternatively.

Now, the result should be divisible by 11, to be divisible by 11.

Let's get an example:

6214813

Divide as a group of three digits from left end, 813, 214, 006

Now, add and substract alternatively

+813 - 214 + 006 = 605, which is divisible by 11.

__11. Divisibility by 12:__

12 = 3×4

If a number is divisible by 3 and 4 both. Then the number is divisible by 12.

Such as, 19044

__12. Divisibility by 13:__

At first, divide numbers from left end as a group of three digits.

Then, sum and substract these groups alternatively.

Now, the result should be divisible by 13, to be divisible by 13.

Let's get an example:

1283685

Divide as a group of three digits from left end, 685, 283, 001

Now, add and substract alternatively

+685 - 283 + 001 = 403, which is divisible by 13.

__13. Divisibility by 14:__

14 = 2×7

If a number is divisible by 2 and 7 both. Then that number will be divisible by 14.

__14. Divisibility by 15:__

15 = 3×5

If a number is divisible by 3 and 5 both, then that number will be divisible by 15.

Such as, 225

Last digit is 5 ; so will be divisible by 5.

Sum of all digits (2+2+5 = 9), is divisible by 3. So will be divisible by 15.

__15. Divisibility by 16:__

If the last 4 digits of a number are divisible by 16, then the whole number is divisible by 16.

Such as, 341920. Here 1920 is divisible by 16; so it will be divisible by 16.

__16. Divisibility by 18:__

18 = 2×9

If a number is divisible by 2 and 9 both, then that number will be divisible by 18.

Here, 5832 is divisible by both 2 and 9. So that number will be divisible by 18.

__Handwritten notes of Divisibility Rule| Divisibility Rule by 7|__

__Important questions of Divisibility Rule:__

Here some important questions on divisibility rule. I hope it will help you a lot.

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