DIVISIBILITY TEST- CBSE Mathematics

__Divisibility Test __:-
**This topic contains the divisibility test by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples for more understanding.**

**Divisibility Test by 2:- **

**· If unit digit of a number is even ( 0, 2, 4, 6, 8) then that number is divisible by “2”**

**· All even numbers are divisible by “2”.**

__Example 1__:-

**· Let given number is 258694**

**· Unit digit of this number is “4” it is even. Therefore 258694 is also divisible by “2”**

__Example 2__:-

**· Let given number is 2586947**

**· Unit digit of this number is “7”, it is odd. So the number 2586947 is not divisible by “2”.**
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test by 3:-**

**· If sum of the digits of a given number is divisible by “3” then that number is also divisible by “3”.**

__Example 1__:-

**· Let given number is :-345897**

**· Sum of the digits: 3+4+5+8+9+7 = 36**

**· 36 is divisible by “3”, so 345897 is also divisible by “3” **

__Example 2__:-

**· Let given number is :- 985897**

**· Sum of the digits: 9+8+5+8+9+7 = 46**

**· 46 is not divisible by “3”, so 985897 is also not divisible by “3” **
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test by 4:-**

**· Take last two digits of of a given number and divide it by “4”, if it is divisible by “4”, then the given number is also divisible by “4”.**

**· If last two digits of a given number is “00” then that number is also divisible by “4”.**

__Example 1__:

**· Let given number is 37984**

**· Last two digits : 8, 4, 84 is divisible by “4”. So 37984 is also divisible by “4”**

__Example 2__:

**· Let given number is 839842**

**· Last two digits : 4, 2, 42 is not divisible by “4”. So 839842 is also not divisible by “4”**

__Example 3__:

**· Let given number is 9739800**

**· Last two digits : 00 , yes 9739800 is also divisible by “4”**

**· If last digits of a given number is either “0” or “5” then the given number is also divisible by “5”.**

__Example 1__:

**· Let given numbers are 379520, 789735**

**· Last digit “0” and “5” . Yes above both numbers are divisible by 5**

__Example 2__:

**· Let given number is 379523**

**· Last digit “3” So above number is not divisible by 5**

**Divisibility Test by 6:-**

**· If a number is divisible by both “2” and “3” then that number is also divisible by 6.**

__Example 1__:

** Let given number is 357846**

**· Last digit is “6”, it is even. So it is divisible by “2”**

**· Sum of the digits: 3+5+7+8+4+6 = 33, “33” is divisible by “3”. So 357846 is also divisible by “3”**

**· Here we find that 357846 is divisible by both “2” and “3”. Hence 357846 is also divisible by “6”**
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test 7:-**

**· Take last digit of a given number.**

**· Now subtract the double of this digit from the remaining number.**

**· Now see whether the result is divisible by "7" or not.**

**· If judgment is still difficult then repeat the above process again and again, till you left with two digit number then make the judgment.**

**Example 1:-**

**· Let given number is 21875**

**· Last digit “5”. Double of 5 is = 10**

**· Now find 2187-10 = 2177**

**· Last digit “7”. Double of “7” is = 14**

**· Now find 217 - 14 = 203**

**· Last digit “3”. Double of 3 is = 6**

**· Now find 20-6 = 14**

**· Since 14 is divisible by “7” so 21875 is also divisible by “7”**

__Example 2__:

**· Let given number is 789423**

**· Last digit “3”. Double of 3 is = 6**

**· Now find 78942 – 6 = 78936**

**· Last digit “6”. Double of 6 is = 12**

**· Now find 7893-12 = 7881**

**· Last digit “1”. Double of 1 is = 2**

**· Now find 788-2 = 786**

**· Last digit “6”. Double of 6 is = 12**

**· Now find 78-12 = 76**

**· 76 is not divisible by “7” so number 35789423 is not divisible by “7”**
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test by 8:-**

**· Take last three digits of a given number and divide it by “8”, if it is divisible by “8” then the given number is also divisible by “8”.**

__Example 1__:

**· Let given number is : 5793512**

**· Last three digits : 5, 1, 2,**

**· 512 is divisible by “8” (512/8 = 64) so 5793512 is also divisible by “8”**

__Example 2__:

**· Let given number is : 5793515**

**· Last three digits : 5, 1, 5,**

**· 515 is not divisible by “8”, so 5793515 is also not divisible by “8”**
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test by 9:-**

**· If sum of the digits of a given number is divisible by “9” then that number is also divisible by “9”.**

__Example 1__:

**· Let given number is : 63918**

**· Sum of the digits: 6+3+9+1+8 = 27**

**· 27 is divisible by “9”, so this number is also divisible by 9”**

__Example 2__:

**· Let given number is : 63925**

**· Sum of the digits: 6+3+9+2+5 = 25**

**· 25 is not divisible by “9”, so number 63925 is also not divisible by “9”**

**Divisibility Test by 10:-**

**· If last digits of a given number is “0” then the given number is also divisible by “10”.**

__Example 1__:

**· Let given number is : 63910**

**· Last digit is “0”, so 63910 is divisible by “10”**

__Example 2__:

**· Let given number is : 63917**

**· Last digit is “7” so 63917 is not divisible by “10”**
DIVISIBILITY TEST- CBSE Mathematics

**Divisibility Test by 11:-**

**· Mark the digits of a given number odd or even, starts from the right side (unit digit).**

**· Add the digits at odd position.**

**· Add the digits at even places.**

**· Find the difference between the two sums.**

**· If difference is either “0” or divisible by “11” then that number is also divisible by 11.**

**· If the difference is not divisible by 11 then that number is not divisible by 11.**

__Example 1__:

**· Let given number is : 659175**

**· Sum of the digits at even place = 7+9+6 = 22**

**· Sum of the digits at odd places = 5+1+5 = 11**

**· Difference: 22-11 = 11**

**· Since difference is divisible by “11” so the number 659175 is also divisible by “11”**

__Example 2__:

**· Let given number is : 959171**

**· Sum of the digits at even place = 1 + 1 + 5 = 7**

**· Sum of the digits at odd places = 7+9+9 = 25**

**· Difference: 25-7= 18**

**· Since difference”18” is not divisible by “11” so the number 959171 is not divisible by “11”**

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