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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