# Short-cuts for division-Divisibility test Tricks

**Division** is one of the basic concepts of **Mathematics** or we can say **Calculation**. Division is easy but it gets complex when we have to find out result for division of higher number. So, here we are going to introduce with **short formulas as well as Divisibility test**. Sometimes, Examiners directly asks about divisibility test of number and we consume so much time in a silly question. Here, we are presenting you some **tricks** so that you don’t speed more than 10-15 seconds to find whether it is divisible by any number form 1 to 10 or not.

## Important Tricks about Divisibility Test

**Divisibility Test**

If examiner asks you question whether x is divisible by y or not. It means they are directly asking for divisibility test.

Divisible by 2

- If last digit (Unit Digit) of any number is even we can say Number is divisible by the 2. ( Rule is Clear, No example needed).

Divisible by 3

- Count sum of all digits of the given number ( if you get sum in two digits, sum again); If result is either 3 or 6 or 9; Number is divisible by 3 otherwise not.

E.g.

Check 9653 is divisible by 3 or not.

As sum of all digits is 23; Sum again, you will get 5 as answer which is not divisible by 3. It means 9653 is not divisible by 3.

Divisible by 4

- If last 2 digit of given number is divisible by 4; entire number is divisible by 4.

E.g.

Check 898128473748 is divisible by 4 or not.

As last two digits of this number is exactly divisible by 4, it means whole number is divisible by 4.

Divisible by 5

- If unit digit (last digit) is either 0 or 5, Number is divisible by 5. (Rule is Clear, No example needed).

Divisible by 6

- First of all check if it is even number. After that, check sum of all digits up to unit digit; if it is either 6 or 9; whole number is divisible by 6.

E.g:

Check 798172895 is divisible by 6 or not.

*As number is odd, it is strictly not divisible by 6.*

Check 7981265376 is divisible by 6 or not.

*As number is odd, apply next step.*

* Sum of all digits is 54 and in unit digit, it is 9. It means whole number is divisible by 6.*

* Cross-check it by your calculator for Confirmation.*

Divisible by 6

- Divide whole number in diff. groups of 3-3 digits starting from the right. Add alternate groups and subtract from each other groups. If difference between groups is 0 or multiple of 7, Number is divisible by 7 otherwise not. (This method is applicable only if number had more 4 or more than 4 digits. )

We know above rule is little bit complex; let’s try to understand it by example.

Check 58556344 is divisible by 7 or not.

**Step 1:**

Divide Number into diff. groups of 3-3 digits starting from the right.

**58-556-344**

**Step 2:**

So sum of alternate groups i.e; First with third and second alone.

First + Third: 344+58= 402

Second: 556

Step 3: Subtract from each other.

556-402= 154

Step 4: Check whether result is divisible by 7 or not.

*As 154 exactly divisible by 7; So above give number is also divisible by 7.*

Divisible by 8

- Rule is too much easy. Just check last 3 digits of given number is divisible by 8 or not. You will come to know whether it is divisible by 8 or not.

Divisible by 9

- This one is also easy. Just check sum of all digits of given number and check whether it is divisible by 9 or not. You will come to know whole number is divisible by 9 or not.

Divisible by 11

- Calculate sum of the alternate digits and check difference between both sums if it is 0 or divisible by 11. Then, the entire number is divisible by 11.

Good Luck……!!!!!