Rules Of Divisibility

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In competitive exams we always get 1-2 questions based on the rules of divisibility in which we need to test if the particular number is divisible by certain number or not. If we actually divide to the test it's divisibility we will kill our precious time so we have certain set of rules by which we can determine the divisibility of a number quicky without much calculation.

Meaning of  divisibility : A number is said to be divisible by another if the result of division is a whole number.

Example : 18 is divisible by 2, because 18÷2 = 9 exactly

But 15 is not divisible by 2, because 15÷2 = 7 1/2 (i.e., the result is not a whole number)    

Divisible By Condition Examples
  2 The last digit should be even (0,2,4,6,8)

142 is Divisible

143 is not Divisible

  3 The sum of the digits should be divisible by 3

1248 is divisible by 3.
(1 + 2 + 4 + 8 = 15)

346 is not divisible by 3.
(3 + 4 + 6 = 13)

 

  4 The last 2 digits should be divisible by 4 1312 is divisible by 4 (12÷4=3)
7019 is not divisible by 4
  5 The last digit should be either 0 or 5

1495 is divisible by 5.
(5 is there at the end)

1234 is not divisible by 5.
(0 or 5 is not there at the end)

  6 The number should be divisible by both 2 and 3

5358 is divisible by 6.
(It is divisible by both 2 and 3)

6782 is not divisible by 6.
(It is divisible by 2 but not divisible by 3)

  7 If  we double the last digit and subtract it from the rest of the number the result should be 0  or divisible by 7.

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No

  8 The last three digits should be divisible by 8

109816 divisible by 8 as
(816÷8=102) 

216302 not divisible by 8 as (302÷8=37 3/4) 

  9 The sum of all the digits should be divisible by 9

1629 is divisible by 9 as (1+6+2+9=18)

2014 not divisible by 9 as (2+0+1+3=7)

  10 The number should end with zero.

110 is divisible by 10

112 not divisible by 10

  11 The difference between the sum of digits at even places and sum of digits at odd places should be 0 or divisible by 11

1364 divisible by 11 as (1−3+6−4 = 0) 

913 divisible by 11 as (9−1+3 = 11) 

987 not divisible by 11 as (9−8+7 = 8)

  12 The number should be divisible by both 3 and 4.

5472 is divisible by 12.
( The number is divisible by both 3 and 4)

5475 is not divisible by 12.
(The number is divisible by 3 but not divisible by 4)

Factor Test for Divisibility: 

Factors are the number that we multiply to get another number so when a number is divisible by another number then it is also divisible by each of the factors of that number.

                                                      Factor Test for Divisibility

Example : If a number is divisible by 6, it is also divisible by 2 and 3

Practice Questions
Q1
Q.no:-1/5