TEST OF DIVISIBILITY

 

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I. Divisibility by 2:

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

EX. (i).567854 is divisible by 2, while 657545 is not divisible by 2.

(ii). 8487576 is divisible by 2, while 8487576 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.(i) In the number 695421, the sum of its digits is divisible by 3.

(ii). In the number 748421, the sum of its digits is divisible by 3.

Therefore,695421, 748421 id divisible by 3.

III. Divisibility by 9 :

A number is divisible by 9 only when the sum of its digits is divisible by 9.

Ex. In the number 246591, the sum of its digits=27 is divisible by 9.

Therefore,246591 is divisible by 9.

IV. Divisibility by 4:

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

Ex. 6879376 is divisible by 4, since 76 is divisible by 4.

Therefore,6879376, is 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. In the number 16789352, the number formed by last 3 digit, namely 352 is divisible by 8.

Therefore,  16789352 is divisible by 8

VI. Divisibility by 10:

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

Ex. 73870 is divisible by 10, since its unit digit i 0.

VII. Divisibility by 5.

A number is divisible by 5 when its unit digit is unit digit is 5 and 0.

Ex. 25  is divisible by 5 as its unit digit is 5.

Ex. 250 is divisible b y 5 as its unit digit is o.

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 digit at even places is either 0r a number divisible by 11.

Ex. Consider the number 2943517

(Sum of its digits at odd places)- (Sum of the digits at even places)

= (7+4+3+9)-(1+5+4+2)

=(23-12)=11

Therefore, 2943517 is divisible by 11

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