Test of Divisibility

Divisibility by 2 

Any number whose last digit is either even number or zero is divisible by 2.

Example: 

• Consider the number 668


•  last digit is  8 which is even


• so 668 is divisible by 2

Divisibility by 3

A number is divisible by 3  if the sum of its digits is divisible by 3 

Example: 

• Consider the number 432


• 4+3+2=9


• 9 is divisible by 3


• so 432 is divisible by 3

Divisibility by 4

If the last two digits of a number are divisible by 4, then that number is  divisible by 4.

Example: 

• consider the number 6424. 

• the last two digits i.e.24. 

• 24 is divisible by 4, 

• so 6424  is  divisible by 4.

Divisibility by 5 

Numbers with last digit 0 or 5 are always divisible by 5.

Example: 645,565,895,650,760 etc.

Divisibility by 6 

Numbers which are divisible by both 2 and 3 are divisible by 6.

Example: ,

• consider the number 540 

• since the last digit is 0 , the number is divisible by 2

• sum of digits 5+4+0=9,  9 is divisible by 3, so 540 is divisible by 3


• since 540 is divisible by both 2 and 3, 540 is divisible by 9

Divisibility by 8 

If the last three digits of a number are divisible by 8, then the number is  divisible by 8.

Example:

• Take number 9240. 


• Consider the last two digits i.e.  240.


•  As 240 is divisible by 8,


•  the original number 9240 is also divisible by 8.

Divisibility by 9

 if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Example:

•  Consider 6543, 


•  the sum of its digits (6+5+4+3) is 18, which is  divisible by 9, 


•  so 6543 is  divisible by 9

Divisibility by 10 

 any number whose last digit is 0, is divisible by 10.

Example: 680,230,3000 etc.

Divisibility by 11

If the difference of the sum of alternative digits of a number is zero or divisible by 11 then that number is divisible by 11 

consider the number 66429

• Group the alternative digits i.e. digits which are in odd places together and digits in even places together. Here 6,4,9 and  6,2 are two groups.


• Take the sum of the digits of each group i.e. 6+4+9=19 and 6+2=8


• Now find the difference of the sums; 19-8= 11


• the difference 11 is divisible by 11


• Therefore, 66429 divisible by 11.

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