DIVISIBILITY RULES - Concept and Examples
Divisibility Rules for the numbers from 11 to 19 , 25 and 125
Divisibility Rule for ‘11’:
A number is divisible by 11 when
the result of subtracting the sum of its digits at odd positions from the sum
of its digits at even positions is either zero or a multiple of 11.
Example 1: 14641,
(Sum of digits at odd places) – (sum
of digits at even places)
( 1 + 6 + 1 ) - (
4 + 4 ) = 0
The difference is 0, the number 14641 is exactly divisible by 11
Example 2 :
The number 4832718 is divisible by
11, Since
(Sum of digits at odd places) – (sum of digits at even places)
( 8 + 7 +
3 + 4 ) - ( 1 + 2 + 8 ) = 11 which is divisible by 11.
Divisibility Rule for ‘12’:
If a number is divisible by both
3 and 4, then it is also divisible by 12.
Example: 1752
In this number, the sum of the digits is (1+7+5+2)=15.
15 is a multiple of 3, so the number is a multiple of 3
1752, the last 2 digits 52 exactly divisible by 4, so the number
is divisible by 4
So the number 1752 is divisible by both 3 and 4, the number
is divisible by 12
Divisibility Rule for ‘13’:
Multiply the last digit of the given number by 4 and add the
product to the remaining part of the number. If the resulting sum is divisible
by 13, then the original number is also divisible by 13. Repeat this process
until a two-digit number is obtained. The final result is a multiple of 13 if
and only if the initial number is a multiple of 13.
Example: 1391 => 139 1 x 4
+
4
143
As 143 is a multiple of 13, the number 1391 is a multiple of 13
Divisibility Rule for ‘14’:
If a number is exactly divisible by both 2 and 7, then the
number is exactly divisible by 14.
Example: 1512, T
1512 is an even number, so it is divisible by 2
Check it by 7, 1512*2
-4
147
147, which is a multiple of 14.
The given number 1512 is exactly divisible by both 2
and 7, so the number is divisible by 7
Divisibility Rule for ‘15’:
If a number is a multiple
of both 3 and 5, the number is a multiple of 15.
Example: 5415
In this number, the sum of the digits is (5+4+1+5)=15.
15 is a multiple of 3, so the number is a multiple of 3
5415, the last digit is 5, so the number is divisible by 5.
So the number 5415 is divisible by both 3 and 5, the
number is divisible by 15
Divisibility Rule for ‘16’:
A number is divisible by 16 if
either the last four digits are all zeroes or the numerical value represented
by the last four digits is a multiple of 16.
Example 1: 725680000 Here last 4 digits are 0's, so
the number is divisible by 16.
Example 2: 7293181680. The numerical value of the last 4
digits is 1680, which is a multiple of 16. So the number is multiple of 16.
Divisibility
Rule for 17
Multiply the last digit of the given number and then subtract
the product from the remaining truncated number. Repeat the step as necessary.
If the result is divisible by 17, the original number is also divisible by 17
Example: Take the number 1938.
193 8 x5
-40
----
153.
Since 153 is divisible by 17, the original number 2278 is also
divisible.
Divisibility
Rule for 18.
If a number is divisible by both 2 and 9, then the number is
exactly divisible by 18
Example: 23526
23526 is an even number, so it is divisible by 2
The sum of the digits of the number 23526 is ( 2+3+5+2+6)=18 which
is divisible by 9.
So 23526 is exactly divisible by both 2 and 9, the number is
divisible by 18.
Divisibility
Rule for 19.
Multiply the last digit of the original number by 2 and then add
the product to the remaining truncated number. Repeat the step as necessary. If
the result is divisible by 19, the original number is also exactly divisible by
19
Example: Let us check for 3895::
389 5x2
+10
-----
39 9x2
+18
-----
57
Since 57 is divisible by
19, the original number 3895 is also divisible by 19.
Divisibility by 25 :
If
the last two digits of a number are
zeroes or the number formed by the last two digits of a number is divisible by
25, then the number is divisible by 25.
Example:
3796800
, 7962175
Divisibility by 125 :
A number is
divisible by 125 if the three-digit number formed by its last three digits is
divisible by 125.
In other
words, if the last three digits of a number are 000, 125, 250, 375, 500, 625,
750, or 875, then the entire number is divisible by 125.
Examples:
3684968375 is
divisible by 125 because the three-digit number formed by its last three digits
375 is divisible by 125
