Divisibility rules for 2,3,4,5,6,7,8,9,10,11 with examples deals with various concepts which are as under:-
- Divisibility Rule for 2
- Divisibility Rule for 3
- Divisibility Rule for 4
- Divisibility Rule for 5
- Divisibility Rule for 6
- Divisibility Rule for 8
- Divisibility Rule for 9
- Divisibility Rule for 10
- Divisibility Test for 11
Divisibility Rules with Examples or Divisibility rules for 2,3,4,5,6,7,8,9,10,11
Divisibility Rule for 2 :-
A number is divisible by 2, if the digit at ones place of that number is divisible by 2 or digit at ones place is 0, 2, 4, 6, 8.
For Example –
Question –
Check whether 2396 is divisible by 2 ?
Solution –
In,2396
6 is at ones place
and 6 is divisible by 2
So,2396 is also divisible by 2
Divisibility Rule for 3 :-
A number is divisible by 3, if the sum of all the digits of the numbers are divisible by 3.
For Example –
Question –
Check whether 23973 is divisible by 3 ?
Solution –
In, 23973
Sum of its digits = 2 + 3 + 9 + 7 + 3 = 24
and 24 is divisible by 3
So, 23973 is also divisible by 3.
Divisibility Rule for 4 :-
A number is divisible by 4, if the number formed by last 2 digits of that number (ones and tens place) is divisible by 4.
For Example –
Question –
Check whether 23924 is divisible by 4 ?
Solution –
In, 23924
24 is the number formed by tens and ones place.
and 24 is divisible by 4.
therefore, 23924 is also divisible by 4.
Divisibility Rule for 5 :-
A number is divisible by 5 if the digit at ones place is either “0” or” 5″.
For Example –
Question –
Check whether 23920 is divisible by 5 ?
Solution –
In, 23920
0 is the digit at ones place
So, 23920 is divisible by 5.
Divisibility Rule for 6 :-
A number is divisible by 6, if it is divisible by both 2 and 3.
For Example –
Question –
Check whether 23724 is divisible by 6 ?
Solution –
Checking Divisibility for 2,
A number is divisible by 2, if the digits at ones place is divisible by 2 or digit at ones place is 0, 2, 4, 6, 8.
In, 23724
4 is at ones place
and 4 is divisible by 2
So, 23724 is also divisible by 2.
Checking Divisibility for 3,
A number is divisible by 3, if the sum of all the digits of the numbers , is divisible by 3.
In, 23724
Sum of digits = 2 + 3 + 7 + 2 + 4 = 18
and 18 is divisible by 3
So, 23724 is also divisible by 3.
Therefore, 23724 is divisible by 2 and 3
Hence, 23724 is also divisible by 6.
Divisibility Rule for 8 :-
A number is divisible by 8, if the number formed by last 3 digits of that number (ones, tens and hundreds place) is divisible by 8.
For Example –
Question –
Check whether 950720 is divisible by 8 ?
Solution –
In, 950720
720 is the number formed by ones, tens, and hundreds place digits or the number formed by last 3 digits .
and 720 is divisible by 8.
Hence, 950720 is also divisible by 8.
Divisibility Rule for 9 :-
A number is divisible by 9, if the sum of all the digits of the numbers is divisible by 9.
For Example –
Question –
Check whether 24597 is divisible by 9 ?
Solution –
In 24597,
Sum of digits = 2 + 4 + 5 + 9 + 7 = 27
27 is divisible by 9
So, 24597 is also divisible by 9.
Divisibility Rule for 10 :-
A number is divisible by 10 if the digit at ones place is 0.
For Example –
Question –
Check whether 23920 is divisible by 10 ?
Solution –
In 23920,
o is at ones place
So, 23920 is divisible by 10.
Divisibility Rule for 11 :-
A number is divisible by 11 if the difference between the sum of the digits at odd place and the digits at even place is either 0 or divisible by 11.
For Example –
Question –
Check whether 73920 is divisible by 10 ?
Solution –
A number is divisible by 11 if the difference between the sum of the digits at odd place and the digits at even place is either 0 or divisible by 11.
In, the given number, 73920
Sum of the digits at even places:
2 + 3 = 5
Sum of the digits at odd places:
0 + 9 + 7 = 16
Difference between sum of digits at odd and even place = 16 – 5 = 11 ( Which is divisible by 11 )
Therefore, 73920 is also divisible by 11