TESTS OF DIVISIBLITY

TESTS OF DIVISIBLITY

I.                    Divisibility by 2 :

 A number is divisible by 2 if its unit digit is any of 0, 2, 4, 6, 8.

Ex. 58694 is divisible by 3.

II.                  Divisibility by 9:

 A number is divisible by 3 only when the sum of its digits is divisible by 3.

 In the numbers 695421, the sum of digits =27, which is divisisible by3.

 695421 are divisible by 3.

(III)             In the number 948653, the sum of digits = 35, which is not divisible by 3.

           948653 is not divisible by 3.

Iv. Divisibility by 4:

A number is divisible by 4 is the sum of its last two digits is divisible by 4.

Ex. (I) 6879376 is divisible by 4, since 76 is divisible by 4.

(II) 496138 is not divisible by 4, since 38 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.

Ex. (I) in the number 16789552, the number formed by last 3 digits namely 352 is divisible by 8.

16789652 is divisible by 8.

(II) in the number 576484, the number formed by last 3 digits, namely 484 is not divisible by 8.

576484 is not divisible by 8.

             VI.            Divisibility by 10:

 A number is divisible by 10 only when its unit digit is 0.

Ex. (I) 7849320 is divisible by 10 only when its unit digit is 0.

(II) 678405 is not divisible by 10, since its unit digit is not 0.

           VII.            Divisibility by 5:

 A number is divisible by 5 only when it s unit digit is 0 or 5.

Ex. Each of the numbers 768405 is not divisible by 10, is divisible by5.

         VIII.            Divisibility by 11:

 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.

 Ex. (I) consider the number 29435417

(Sum of its digits at odd places) – (sum of it s digit s at even places)

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

A: 29435417 are divisible by 11.

(II) Consider the number 57463822.

(Sum if its digits at odd places) – (sum of its digits at even places)

= (2+ 8 + 6+ 7)- (2 + 3 + 4 + 5)= (23 - 14)=9, which is not divisible by 11.

A: 57463822 are not divisible by 11.