Assorted Divisibilty Rules

Assorted Divisibility Rules :-

I ) Divisibility By 2 : A number is divisible by 2 if its unit is any of 0 ,2 ,4 , 6 , 8 .


Ex. 86354 is divisible by 2 , while 673453 is not divisible by 2.


II) Divisibility By 3 : A number is divisible by 3 only when the Sum of its digits is


divisible by 3 .


Ex. a) In the number 765432 ,the Sum of its digits = 27 , which is divisible by 3 .


Hence 765432 is divisible by 3 .


b) In the number 489365 ,the Sum of its = 35 ,which is not divisible by 3 .


Hence 489365 is not divisible by 3 .


III) Divisibility By 9 : A number is divisible by 9 only when the Sum of its digits is


divisible by 9 .


a) In the number 246591 ,the Sum of its digits = 27 , which is divisible by 9 .


Hence 246591 is divisible by 9 .


b) In the number 437915 ,the Sum of its digits = 29 ,which is not divisible by 9.


Hence 437915 is not divisible by 9.


IV) Divisibility By 4 : A number is divisible by 4 if its last two digits is divisible by 4.


a) 8769376 is divisible by 4 , since 76 is divisible by 4.


b) 694139 is not divisible by 4 , since 39 is not divisible by 4 .


V) Divisibility By 8 : A number is divisible by 8 if the number formed by hundred's


,ten's and unit's digit of the given number is divisible by 8 .


a) In the number 76189352 , the number formed by last 3 digits , namely 352 is


divisible by 8.


Hence 76189352 is divisible by 8 .


b) In the number 756484 , the number formed by last 3 digits , namely 484 is


not divisible by 8 . Hence 756484 is not divisible by 8 .


VI ) Divisibility By 10 : A number is divisible by 10 only when its unit digit is 0.


a) 7849320 is divisible by 10 only , since its unit digit is 0 or 5 .


b) 8765138 is not divisible by 10 since its unit digit is not 0 .


VII) Divisibility By 5 : A number is divisible by 5 only when its unit digit is 0 or 5 .


a) Each of the numbers 869765 and 452365 is divisible by 5 .


VIII) A number is divisible by 11 if the difference between the Sum of its digits at


odd places and the Sum of its digits at even places is either 0 or a number


divisible by 11 .


a) Consider the number 29435417 ( Sum of its digits at odd places ) -


( Sum of its digits at even places )



= ( 7+4+3+9) - ( 1+5+4+2) = (23 - 12) = 11 ,which is divisible by 11 .


Hence 29435417 is divisible by 11*