Divisibility Rules for 2, 3, 4, 5, 6, 8, 9, 10, 11 – Examples | Maths

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

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