# Divisibility Rule for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

__Divisibility Rule__

## How to test number is completely divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

### Rules to divide by 2

If the unit digit of a number is any of 0, 2, 4, 6, 8 then that number will be divided by 2.

**Example-**Each of the following numbers will be completely divisible by 2.

68761

__2__, 98759__8__, 9658__4__, 589__6__, 6731__0__

### Rules to divide by 3

If the sum of all digits of a given number is completely divisible by 3, then that number will be completely divisible by 3.

**Example-**(i) 57351

Sum of digits= (5+7+3+5+1) = 21, which completely divisible by 3.

So, the given number is completely divisible by 3

### Rules to divide by 9

If the sum of all digits of a given number is completely divisible by 9, then that number will be completely divisible by 9.

**Example-**(i) 451827

Sum of digits= (4+5+1+8+2+7) = 27, which completely divisible by 9.

So, the given number is completely divisible by 9.

➡ 9^{(Odd power)}, when divided by 10, always gives 9 as the remainder.

➡ 9^{(Even power)}, when divided by 10, always gives 1 as the remainder.

### Rules to divide by 5

If the given number unit digit is 5 Or 0, then that number will be completely divisible by 5.

**Example-**(i) 45182

__5__and 6893

__0__are completely divisible by 5.

### Rules to divide by 10

If the given number unit digit is 0, then that number will be completely divisible by 10.

**Example-**5641

__0__, and 6598

__0__are completely divisible by 10.

### Rules to divide by 4

A given number will be divisible by 4 only when the number formed by its tens and unit digits (Last to digits) is completely divisible by 4.

**Example-**(i) 5768

__32__

The number formed by its tens and unit digits is 32, which will be completely divided by 4.

Hence the given number 576832 will be completely divisible by 4.

### Rules to divide by 8

A given number will be divisible by 8 only when the number formed by its unit, tens and hundred digits (Last three digits) is completely divisible by 8.

**Example-**(i) 654

__512__

The number formed by its tens and unit digits is 512, which will be completely divided by 8.

Hence the given number 654512 will be completely divisible by 8.

### Rules to divide by 6

A given number will be divisible by 6 only if it is divisible by 2 and 3.

**Example- 897**

__6__, 6513__6__Both numbers are divisible by 2 and 3.

### Rules to divide by 7

The number is obtained by doubling the unit digit and subtracting it from the remaining number, if it is divisible by 7, then the given number becomes divisible by 7.

**Example-**(i) 882

(88 - 2 ✕ 2) = 84 which completely divisible by 7.

Hence the given number 882 will be completely divisible by 7.

(ii) 663

(66 - 2 ✕ 3) = 60 which completely divisible by 7.

Hence the given number 663 will be completely divisible by 7.

### Rules to divide by 11

The given number will be divisible by 11 only if the difference between the sum of the digits of the even-places and the sum of the digits of the odd-places is 0 or a multiple of 11.

**Example-**(i) 901219

( sum of the digits of the odd-places) - (sum of the digits of the even-places)

= ( 9+2+0 ) - (1+1+9 )

= (11 - 11 ) = 0

Hence the given number 901219 will be completely divisible by 11.

(ii) 82735213

(sum of the digits of the even-places) - ( sum of the digits of the odd-places)

= ( 1+5+7+8 ) - ( 3+2+3+2 )

= ( 21 - 10 )

= 11

Hence the difference is 11, which is completely divisible by 11 then the given number 82735213 will be completely divisible by 11.

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