Divisibility Rules :
(From 1 to 20)



Divisibility rules are most important part in simplify any sums. If you know divisibility rules of a number , you can calculate any sums fast and easily. It is very helpful to crack exam very easily and fast. 

Divisibility rules is also most important topic in competitive exams like SSC, RRB, UPSC, IBPS any other state level exams. 

Here, we have provided you, Divisibility rules for 1 to 20 .

Divisibility rules for 1 to 20

➤ Divisibility Rule of 1

      "Any Integer is divisible by 1."

 

➤ Divisibility Rule of 2

       “A number is divisible by 2, if its last digit is any of 0, 2, 4, 6, or 8.”


Ex. 84394 is divisible by 2.

      26537 is not divisible by 2.

 

➤ Divisibility Rule of 3

        “A number is divisible by 3, if sum of the all digits is divisible by 3.”


Ex. 432582 is divisible by 3,
      Since sum of all digits (4+3+2+5+8+2=24) is divisible by 3.

Ex. 256933 is divisible not by 3,
      Since sum of all digits (2+5+6+9+3+3=26) is not divisible by 3.

➤ Divisibility Rule of 4

    “A number is divisible by 4, if the number formed by last two digits is divisible by 4.”


Ex. 357124 is divisible by 4, 
      Since the number formed by last two digits (24) is divisible by 4.
Ex. 653482 is not divisible by 4, 
      Since the number formed by last two digits (82) is not divisible by 4.

➤ Divisibility Rule of 5

    “A number is divisible by 5, if its unit’s digit is either 0 or 5.”


Ex. 25820, 637925 are divisible by 5.
      30526, 965248 are not divisible by 5.

➤ Divisibility Rule of 6

     “A number is divisible by 6, if it’s divisible by both 2 and 3.”


Ex. 53724 is divisible by 6,
    • Since last digit is 4, so it’s divisible by 2,
    • And sum of all digits is (5+3+7+2+4=21) is divisible by 3. 
Thus, 53724 is divisible by 2 and 3 both, so it is divisible by 6.

➤ Divisibility Rule of 7

    “Double the last digit and subtract it from a number made by the remaining digits (you can repeat the step again). If the result is 0 or divisible by 7 then the given number is divisible by 7.” 

Ex. 595 is divisible by 7, since double of 5 is 10, 
       and 59-10 =49 is divisible by 7 so 595 is divisible by 7. 

   • 1743 is divisible by 7, since double of 3 is 6, 
       and 174-6 =168, repeat step again double of 8 is 16 
       and 16-16=0 , so 1743 is divisible by 7.

➤ Divisibility Rule of 8

     “A number is divisible by 8, if the number formed by last three digits of the given number is divisible by 8.”


Ex. 785624 is divisible by 8,
      Since the number formed by last three digits is 624 which is divisible by 8, 
      So 785624 is divisible by 8. 

➤ Divisibility Rule of 9

    “A number is divisible by 9, if sum of the all digits is divisible by 9.”


Ex. 451836 is divisible by 9,
Since sum of all digits (4+5+1+8+3+6=27) is divisible by 9.

Ex. 256927 is divisible not by 9,
Since sum of all digits (2+5+6+9+2+7=31) is not divisible by 9.

➤ Divisibility Rule of 10

     “A number is divisible by 10, if its unit’s digit is 0.”


Ex. 65480, 317250 are divisible by 10.
      105005, 20005 are not divisible by 10.

➤ Divisibility Rule of 11

  “A number is divisible by 11, if the difference of sums of digits at odd place and sum of digits at even place is 0 or divisible by 11.”


Ex. 35417 is divisible by 11,
        Since (sum of digits at odd place) - (sum of digits at even place) 
                 = (7+4+3) - (1+5)
                 = 17-6 
                 = 11, which is divisible by 11
Thus 35417 is divisible by 11.

➤ Divisibility Rule of 12

     “A number is divisible by 12, if it is divisible by both 4 and 3.” 


Ex. 34632 is divisible by 12,
     •Since number formed by last two digits is 32, which is divisible by 4.
     •Sum of all digits (3+4+6+3+2=18) is divisible by 3

Thus 34632 is divisible by both 4 and 3, so it is divisible by 12.


➤ Divisibility Rule of 13

      “A number is divisible by 13, if addition of 4 times the last digit and number formed by the remaining digits is divisible by 13."

(Repeat the step again until you get two digit numbers.)


Ex. 1625 is divisible by 13, 
       Since 4 times of 5 is 20, and remaining digits are 162
      162+20=182, repeat step again
      18+(4x2)=26, which is divisible by 13
      So 1625 is divisible by 13.

➤ Divisibility Rule of 14

     “A number is divisible by 14, if it is divisible by both 2 and 7.” 

Ex. 4872 is divisible by 14,

     • Since last digit is 2, which is divisible by 2.
     • Double of the last digit 2 is 4, and 487-4=483
       Repeating step again, double of last digit 3 is 6, 
       and 48-6=42, which is divisible by 7.

Thus 4872 is divisible by both 7 and 2, so it is divisible by 14.

➤ Divisibility Rule of 15

    “A number is divisible by 15, if it is divisible by both 5 and 3.” 

Ex. 8235 is divisible by 15,
      • Since last digit is 5, so it is divisible 5.
      • Sum of all digits (8+2+3+5=18) is divisible by 3.

Thus 8235 is divisible by both 5 and 3, so it is divisible by 15.

➤ Divisibility Rule of 16

     “A number is divisible by 16, if the number formed by last four digits of the given number is divisible by 16.”


Ex. 7957536 is divisible by 16,
Since the number formed by last four digits is 7536, which is divisible by 16.

Thus 7957536 is divisible by 16. 


➤ Divisibility Rule of 17

     “Five times of the last digit and subtract it from a number formed by the remaining digits (you can repeat the step again). If the result is 0 or divisible by 17 then the given number is divisible by 17.” 


Ex. 646 is divisible by 7, since five times of 6 is 5x6=30, 
      and 64-30=34 is divisible by 17, 
      so 646 is divisible by 17.

      5542 is divisible by 17, since 2x5=10, 554-10 =544, repeat step again.
      5x4=20 and 54-20=34, which is divisible by 17.
      So 5542 is divisible by 17.


➤ Divisibility Rule of 18

     “A number is divisible by 15, if it is divisible by both 2 and 9.” 


Ex. 53766 is divisible by 18,
      • Since last digit is 6, so it’s divisible by 2,
      • And sum of all digits (5+3+7+6+6=27) is divisible by 9.
 Thus, 53766 is divisible by 2 and 9 both, so it is divisible by 18.

➤ Divisibility Rule of 19

       “A number is divisible by 19, if addition of double of last digit and number   formed by the remaining digits is divisible by 19."

 (Repeat the step again until you get two digit numbers.)


Ex. 1425 is divisible by 19, 
      Since double of 5 is 10 and remaining digits are 142.
      142+10=152, repeat step again
      15+(2x2)=19,  which is divisible by 19.
      So 1425 is divisible by 19.

➤ Divisibility Rule of 20

    “A number is divisible by 20, if the number formed by last two digits is divisible by both 5 and 4.”


Ex. 57480 is divisible by 20, 
       Since last two digits 80 is divisible by both 5 and 4.