Monday, 15 June 2015

Divisibility rules


        If we want to find a particular number whether divisable by a particular number faster most preferably in competitive exams this is very useful. Here are some divisibility rules.

Divisibility by 2 rule
A number is divisible by 2 if its unit digit is 0,2,4,6,8.
Eg:-98740 is divisable by 2 as its unit digit is 0.

Divisibility by 3 rule
A number is divisable by 3 when the sum of its digits is divisable by 3.
Eg:-6324 is divisable by 3 (6+3+2+4=15, which is divisable by 3).

Divisibility by 4 rule
A number is divisible by 4 if the number’s last two digits are divisible by 4.
Eg:-9824 is divisable by 4 because last two digits 24 is divisable by 4.

Divisibility by 5 rule
A number is divisible by 5 if unit digit is 0 or 5.
Eg:-7840 is divisible by 5 as its unit digit is 0.

Divisibility by 6 rule
A number is divisible by 6 if it is divisible by 2,3.
Eg:-114 is divisible by 6 as it is divisible by both 2 and 3.

Divisibility by 7 rule
To check if a number is divisible by 7 we should Double the last digit, then subtract result from the rest of the digits. Repeat for larger numbers until result is a 2-digit number
Eg:-7357 is divisible by 7 as last digit=7,7*2=14.
                          Then subtract 14 from 735=721.
                                                            1*2=2
                              Then subtract 2 from 72=70
Now the two digit number 70 is divisible by 7, (7*10=70).

Divisibility by 8 rule
A number is divisible by 8 if the last three digits is divisible by 8.
Eg:-9640 is divisible by 8 (640/8=80).

Divisibility by 9 rule
A number is divisible by 9 if the sum of digits are evenly divisible by 9.
Eg:-4518 is divisible by 9 (4+5+1+8=18,18/9=2)

Divisibility by 10 rule
A number is divisible by 10 if its unit digit is 0.
Eg:-5960 is divisible by 10, while 5965 is not divisible by 10.

Divisibility by 11 rule
A number is divisible by 11 if the difference of sums of alternating digits is 0 or divisible by 11.
Eg:-10813 is divisible by 11 as (1+8+3)-(0+1)=11.which is divisible by 11.

Divisibility by 12 rule
A number is divisible by 12 if it is divisible by both 3 and 4.
Eg:-648 is divisible by 12 as (6+4+8=18 divisible by 3),(12*4=48 divisible by 4)

Divisibility by 13 rule
If a number must be divisible by 13 we must multiply the unit digit of the given number with 4 and add to truncated no. repeat the process till we get small no.
Eg:-936=6*4=24,93+24=117(7*4=28)
=11+28=39
As 39 is divisible by 13 (13*3), the whole number 936 is divisible is by 13.

Divisibility   by 14 rule
If a number is divisible by 2 and 7 it is divisible by 14
Eg:-42 is divisible by 14 as it is divisible by both 2 and 7(unit digit 2 is divisible by 2)(42 is divisible by 7)

Divisibility by 15 rule
A number is divisible by 15 if it is divisible by 3 and 5.
Eg:-435 is divisible by 15 as it is divisible by both 3&5
(4+3+5=12;12 is divisible by 3), (unit digit is 5 so divisible by 5)

Divisibility by 16 rule
If the thousands digit is even take the last three digits. If the thousands digit is odd, add 8 to the last three digits. With the 3-digit number, multiply hundreds digit by 4, then add the last two digits.
Eg:- 254,176: Thousands digit = 4, so take 176 (1 × 4) + 76 = 80 80 = 5 x 16
       693,408: Thousands digit = 3, 408 + 8 = 416 (4 x 4) + 16 = 32, 32 = 2 x16

Divisibility by 17 rule
If  we subtract 5 times the last digit from the rest.
Eg:-221 is divisible by 17 as 22-(1*5)=17.

Divisibility by 18 rule
If a number is divisible by 2 and 9 it is divisible by 18.
Eg:-54 is divisible by 18 as it is divisible by 2&9
(unit number 4 is divisible by 2); (5+4=9 divisible by 9)

Divisibility by 19 rule.
If a number must be divisible by 19 we should add twice the last digit to the rest
Eg:-437 is divisible by 19 as 43 + (7 × 2) = 57; 5 + (7 x 2) = 19

Divisibility by 20 rule
Divisible by 10 and the tens digit is even.
 Eg:-360 is divisible by 20 as last digit = 0 and 6 is even.

Note:-
If a number a is divisible by another number x then it is divisible by the other factors of x.
Eg:-we know that 24 is divisible by 12.
Therefore 24 is also divisible by all the other factors of 12.(1,2,3,4,6) 

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