Test For Divisibility Of Numbers

DIVISIBILITY TEST
(a)     Divisibilit by 2 : A given number is divisible by 2, if its unit digit is any of 0, 2, 4, 6, 8 e.g. 4268134 is divisible by 2 while 311267429 is not divisible by 2. 

(b)    Divisibility by 3 : A number is divisible by 3, if sum of its digits is divisible by 3 e.g. 252771 is divisible by 3 as sum of its digits (2 + 5 + 2 + 7 + 7 + 1 = 24) is divisible by 3.

(c)    Divisibility by 4 : A number is divisibly by 4 if the last two digits of the number is divisible by 4 or the number ends with '00'. e.g. 213428 is divisible by 4 as last two digits is 28 which is divisible by 4. 1246800 is also divisible by 4 as the number ends with 00.

(d)    Divisibility by 5 : A number is divisible by 5 if its unit place digit is either 0 or 5.

(e)    Divisibility by 6 : A number is divisible by 6 if it is divisible by 2 and 3 both. e.g., 254784 is divisible by 6 because it is an even number and hence divisible by 2, also the sum of digits  i.e., 2 + 5 + 4 + 7 + 8 + 4 = 30 is divisible by 3. Hence the number is divisible by 6.

(f)    Divisibility by 8 : A given number is divisible by 8 if the number formed by last three digits of the number is divisible by 8 or the number ends with '000' e.g., 342840 is divisible by 8 because 840 is divisible by 8. 29342000 is also divisible by 8.

(g)    Divisibility by 9 : A number is divisible by 9 if the sum of digits of the number is divisible by 9. e.g. 284796 is divisible by 9 because sum of digits 2 + 8 + 4 + 7 + 9 + 6 = 36 is completely divisible by 9.

(h)    Divisibility by 10 : A number is divisible by 10 if the unit place digit of given number is '0' e.g., 21380, 3142900 are divisible by 10, whereas 214385, 329212, 46843 are not divisible by 10.

(i)    Divisibility by 11 : A number is divisible by 11 if the difference between the sum of the digits in the odd places and the sum of the digits in the even places is either O or completely divisible by 11. e.g., 6584919 is divisible by 11 because. (Sum of digits at odd places) – (Sum of digits at even places)
⇒     (6 + 8 + 9 + 9) – (5 + 4 + 1)
⇒     32 – 10 = 22, which is divisible by 11.

(j)    Divisibility by 12 : If a given number is divisible by both 3 and 4 then it is also divisible by 12 e.g., 16128 is divisible by both 3 and 4 and hence it is divisible by 12 also.