Divisibility Rules - Concept
Divisibility rules are
useful to find whether a number is exactly divisible by another number or not
without performing actual division.
Divisibility Rule For 0:
Division by zero is not defined
Divisibility Rule For 1:
Every number is divisible by 1
Divisibility Rule for 2:
if the last digit of a number is 0 or 2 or 4
or 6 or 8 i.e., divisible by 2, then the number is divisible
by 2.
Example: 123456, 208, 304…
Divisibility Rule for 3:
If the sum of all digits of a number is divisible by 3, the
number is also divisible by 3.
Example:- 1731
In the number 1731, the sum of the digits is 1+7+3+1=12,
which is exactly divisible by 3. So 1731 is also divisible by 3.
Example: 825, 1362, 1233…
Divisibility Rule for 4:
If the last two digits of a number are zeros or the number
formed by the last 2 digits is divisible by 4, then the number is divisible by
4.
Example: 31428, 44300….
Divisibility Rule for 5:
If the last digit of a number is 0 or 5, then the number is
exactly divisible by 5.
Example: 400, 405, 1055…
Divisibility Rule for 6:
If a number is exactly divisible by both 2 and 3, then the
number is divisible by ‘6’ also.
Example: 324, 1254
If we take the number 216,
216 is an even number, so
it is divisible by 2
And the sum of the digits is 2+1+6 =9, which is a multiple
of 3.
So the number 216 is a multiple of both 2 and 3 then the number is
exactly divisible by 6.
Divisibility Rule for ‘7’:
Subtract twice the last digit
from the remaining part of the number, and repeat the process until a
single-digit number is obtained. If the final result is divisible by 7
(including 0), then the original number is also divisible by 7. The outcome
will be 7, 0, or -7, only if the initial number is a multiple of 7.
Example: 371
371×2
-2
------
35
35 is divisible by 7. The given number 371 is also divisible
by 7
Divisibility Rule for ‘8’:
If the number formed by the last
three digits of a number is divisible by 8 or if the last 3 digits of a number
consist of three zeros, then the entire number is divisible by 8.
For instance, in the number 27358128, since the last three digits, 128, are
divisible by 8, the entire number 27358128 is divisible by 8.
Divisibility Rule for ‘9’:
The rule for divisibility by 9
states that if the sum of all the digits in a number is divisible by 9, then
the entire number is also divisible by 9.
For example, in the number
172845, the sum of its digits (1+7+2+8+4+5) equals 27, which is a multiple of
9. Therefore, the number 172845 is divisible by 9.
Divisibility Rule for 10:
If the last digit of a number is ‘0’ then the number is divisible by 10.
Example: 1000, 2120…
