DIVISIBILITY RULES 1 TO 10

In this section, you will learn the shortcuts (rules) to check whether a number is evenly divisible by another number without doing too much calculation. 

Once we remember these rules, we can do division of numbers easily without calculator.r

Divisibility Rule for 2

All even numbers are divisible by 2.

A number  ends with one of the following digits is called as even number.

0, 2, 4, 6 or 8 

Divisibility Rule for 2 - Example

Problem :

Check whether 16 is divisible by 2. 

Solution :

16 ends with the digit 6.

So, it is even number and it divisible by 2. 

Divisibility Rule for 3

To check whether a number is divisible by 3, we have to find the sum of the digits in the number.

If the sum of the digits is divisible by 3 or multiple of 3, then the number is divisible by 3. 

Divisibility Rule for 3 - Example

Problem : 

Check whether 252 is divisible by 3.

Solution :

Add all the digits in the number 252.

2 + 5 + 2  =  9

The sum of the digits in the given number 252 is 9 which is a multiple of 3. 

So, 252 is divisible by 3. 

Divisibility Rule for 4

If the last two digits of a number are zeroes or the number formed by the last 2 digits is divisible by 4, then the number is divisible by 4.

Divisibility Rule for 4 - Example

Problem : 

Check whether 328 is divisible by 4.

Solution :

In the given number 328, the last two digits are not zeroes.

But, the number formed by the last two digits is 28 which is divisible by 4. 

So, the given number 328 is divisible by 4.

Divisibility Rule for 5

If a number ends with 0 or 5, then it is divisible by 5. 

Divisibility Rule for 5 - Example

Problem :

Check whether 105 is divisible by 5.

Solution :

The given number 105 ends with 5. 

So, the given number 105 is divisible by 5.

Divisibility Rule for 6

If a number is divisible by both 2 and 3, then it is divisible by 6.

We already know that all even numbers are divisible by 2.

So, all even numbers which are divisible by 3 are divisible by 6. 

Divisibility Rule for 6 - Example

Problem : 

Check whether 5832 is divisible by 6.

Solution :

The given number 5832 ends with 2.

So, it is even number and divisible by 2.

Check whether the number 5832 is divisible by 3. 

Add all the digits.

5 + 8 + 3 + 2  =  18 

The sum of the digits in the given number 5832 is 18 which is a multiple of 3.

Therefore, the given number 5832 is divisible by both 2 and 3.

So, the given number 5832 is divisible by 6. 

Divisibility Rule for 7

In a number, if the difference between twice the digit in one's place and the number formed by other digits is either zero or a multiple of 7, then the number is divisible by 7. 

Divisibility Rule for 7 - Example

Problem : 

Check whether 504 is divisible by 7. 

Solution :

Twice the digit in one's place is

=  2 ⋅ 4

=  8

The number formed by the digits except the digit in one's place is

=  50

The difference between twice the digit in one's place and the number formed by other digits is 

=  50 - 8

=  42

42 is divisible by 7.

So, the given number 504 is divisible by 7. 

Divisibility Rule for 8

In a number, if the last three digits are zeros or the number formed by the last 3 digits is divisible by 8, then the number is divisible by 8.

Divisibility Rule for 8 - Example

Problem : 

Check whether 789516 is divisible by 8. 

Solution :

In the given number 789516, the last three digits are not zeroes.

But, the number formed by the last three digits is 516 which is divisible by 8. 

So, the given number 789516 is divisible by 8.

Divisibility Rule for 9

If the sum of the digits of a number is divisible by 9 or multiple of 9, then it is divisible by 9. 

Divisibility Rule for 9 - Example

Problem : 

Check whether 12708 is divisible by 9. 

Solution :

Add all the digits in the number 12708.

1 + 2 + 7 + 0 + 8  =  18  

The sum of the digits in the given number 12708 is 18 which is a multiple of 9. 

So, 12708 is divisible by 9. 

Divisibility rule of 10

If a number ends with 0, then it is divisible by 10.

Examples :

10, 40, 300, 500, 450

Divisibility Rule for 10

Problem :

Check whether 9470 is divisible by 10. 

Solution :

The number 9470 ends with 0.

So, it is divisible by 10.

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