Any number is divisible by 2 , if the last number is even . So if the last digit of a number is 0,2,4,6 or 8 it is divisible by 2

Some of the numbers which are divisible by 2 are 84, 686, 7550, 25684 ( all these numbers have even numbers as their last digit)

If the sum of the digits of the number is divisible by 3 , so is the number . In other words , just add the digits , if that can be divided by 3, the number will also be.

How about trying this rule on 315
The sum of the digits is 3 + 1 + 5 = 9
Now 9 is divisible by 3 ( 9 / 3 = 3)
So 315 is also divisible by 3

If the last two digits of any number are divisible by 4 , then the number also is divisible by 4.

Let’s check this out on 6536
The last two digits of 6536 is 36
Now 36/ 4 = 9 As 36 is divisible by 4
So 6536 is divisible by 4

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

How about 26580, it  can be divisible by 5 , as its last digit is 0.

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

Let’s try it with 726 , we find whether it is divisible by 2 and 3
726/2=363 & 726/3=242
As 126 is divisible by both 2 and 3
So it is divisible by 6 also

To find whether a number is divisible by 7 or not , take the last digit , double it ,and subtract it from the rest of the number , if the answer is divisible by 7 ( including 0) , then the number is also divisible by 7

Is 175 divisible by 7
Here the last digit is 5 , we double it , that is 10
Now 10 is subtracted from 17
17 - 10 = 7
As 7 is divisible by 7, so also 175

If the last three digits of the number are divisible by 8, so is the number .

How about 652424
In this case the last three digits are 424
now as 424/8 =53
So 652424 is also divisible by 8

If the sum of the digits is divisible by 9 , the number will also be.

Let’s check it with 612
Here sum of the digits is 6 + 1 + 2 = 9
which is divisible by 9
So 612 is divisible by 9

  Any number which ends in 0 , is divisible by 10 .

To test whether a number is divisible by 11 or not , alternately add and subtract the digits from left to right . If the result ( including 0) is 0, then the number is also divisible

Let us take an example: 3267
3 - 2 +  6 - 7= 0,
So 3267 is divisible by 11