# Math Help - Tests of Divisibility- Simple tricks

1. ## Tests of Divisibility- Simple tricks

With this simple short cuts you can find out a number is divisible by a given number
Divisible by 2: A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8.
Example: 6798512

Divisible by 3: A number is divisible by 3, if sum of its digits divisible by 3.
Example : 123456
1+2+3+4+5+6 = 21
21 is divisible by 3 so 123456 is also divisible by 3

Divisible by 4: if the last two digits of a given are divisible 4, so the number can be divisible by 4.
Example : 749232
Last two digits are 32 which are divisible by 4 so the given number is also divisible by 4

Divisible by 5: If unit’s digit of a number is either ‘0’ or ‘5’ it is divisible 5.
Example : 749230

Divisible by 6: If a given number is divisible by 2 and 3 (which are factors of 6), then the number is divisible by 6.
Example : 35256
Unit’s digit is 6 so divisible by 2
3+5+2+5+6 = 21 so divisible by 3
So 35256 divisible by 6

Divisible by 8: if last 3 digits of a given number is divisible 8, then the given number is divisible 8.
Example: 953360
360 is divisible by 8, so 953360 is divisible by 8

Divisible by 9: A number is divisible by 9, if sum of its digits divisible by 9.
Example : 50832
5+0+8+3+2 = 18 divisible by 9 so 50832 divisible by 9

Divisible by 10: A number is divisible 10, if it ends with 0.
Example : 508320

Divisible by 11: A number is divisible by 11,if the difference of sum of its digits at odd places and sum of its digits at even places , is either 0 or a number divisible by 11.
Example : 4832718
(sum of digits at odd places ) – (sum of digits at even places)
=(8+7+3+4)-(1+2+8) = 11 which is divisible by 11.
So 4832718 is divisible by 11.

I hope this simple tricks, will be very helpful to solve math’s homework problems easily.

2. ## Re: Tests of Divisibility- Simple tricks

Divisible by 7

Subtract twice the unit-digit from the 'rest of the number'.
If the result is divisible by 7, the number is divisible by 7.

Example: .Is $903$ divisible ny $7$?
We have: . $90 - (2\cdot3) \:=\:84$
. . Since $84$ is divisible by $7$, then $903$ is divisible by $7.$

The procedure can be repeated for larger numbers.

Example: .Is $8813$ divisible by $7$?
. . We have: . $881 - 6 \:=\:875$
Is $875$ divisible by $7$?
. . We have: . $87-(2\cdot5) \:=\:77$
Since $77$ is divisible by $7$, then $8813$ is divisible by $7.$

3. ## Re: Tests of Divisibility- Simple tricks

Originally Posted by Soroban

Divisible by 7

Subtract twice the unit-digit from the 'rest of the number'.
If the result is divisible by 7, the number is divisible by 7.

Example: .Is $903$ divisible ny $7$?
We have: . $90 - (2\cdot3) \:=\:84$
. . Since $84$ is divisible by $7$, then $903$ is divisible by $7.$

The procedure can be repeated for larger numbers.

Example: .Is $8813$ divisible by $7$?
. . We have: . $881 - 6 \:=\:875$
Is $875$ divisible by $7$?
. . We have: . $87-(2\cdot5) \:=\:77$
Since $77$ is divisible by $7$, then $8813$ is divisible by $7.$
Thank you for this divisibility by 7 test
Here is a quick proof

$(10x+d)-10(x-2d)=21d$