Divisibility Rules

Divisible by 2

If the unit digit of the number is even then the number is divisible by 2.

or

Any number whose unit digit is 0, 2, 4, 6 or 8 then the number is divisible by 2.

example: 892, 3648, 7936, 5566914, 22340 etc.

Divisible by 3

If the sum of all digits of a number is divisible by 3, then the number is divisible by 3.

example: 

i) 897121

sum of unit digits 8+9+7+1+2+1=28

since 28 is not divisible by 3, 897121 is not divisible by 3.

ii) 562137

sum of digits 5+6+2+1+3+7=24

since 24 is divisible by 3, 562137 is also divisible by 3.

Divisible by 4

If the last two digits of a number is divisible by 4, then the number is divisible by 4. 

Last two digits of the number can be 00, 04, 08, 12, 16, 20, 24...,96

example: 764, 82540, 369292, 879684, etc.

Divisible by 5

If the last digit of a number is either  5 or 0, then the number is divisible by 5.

example: 110, 265, 33845, etc.

Divisible by 6

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

Or

The even number which is divisible 3 is also divisible by 6.

example: 8640, 7656, 105936 etc.

Divisibility by 7

Multiply the digit of unit place by 2 and subtract from the remaining part of that number. If the resultant number is divisible by 7 then the number is divisible by 7.

example:- 

i) 405

The unit digit is 5 and remaining part of the number is 40.

40-5*2=30

since 30 is not divisible by 7, 405 is also not divisible by 7.

ii) 924

The unit digit is 4 and remaining part of the number is 92.

92-4*2=84

7 divides 84, so 924 is also divisible by 7.

Divisibility by 8

If the number formed by the last three digit of the given number is divisible by 8 then the actual number is divisible by 8.

The last three digit of the number can be 000,008,016,032,064,....,096,104,112,.....,992.

example:-

889344

number formed by last three digit of the given number is 344.

Since 344 is divisible by 8.

Hence 889344 is divisible by 8.

Divisibility by 9

If the sum of digits of the given number is divisible by 9, then the number is divisible by 9.

example:

i) 986321

sum of digits is 9+8+6+3+2+1=29

since 29 is not divisible by 9, hence 986321 is also not divisible by 9.

ii) 7648128

sum of digits 7+6+4+8+1+2+8=36

since 36 is divisible by 9, hence 7648128 is also divisible by 9.

Divisibility by 10

If the last digit of the number is zero, then the number is divisible by 10.

example: 70, 1520, 3548520 etc.

For any query comment below.

Thank you.

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