When you are in a hurry and you want to quickly determine, if a number can be divided by 2, 4, 6, 7, 8, 9 without long division then divisibility rules comes into rescue where you can test easily if one number can be evenly divided by another.

Divisibility means that you are able to divide a number evenly.

Divisibility rule is used to check whether a given number is divisible by a fixed divisor by examining its digits.

To illustrate the concept, Suppose you are in a coffee shop and you have ordered 8 cups of coffee. You and your 3 friends wish to have 2 cups of coffee each. Suddenly one of your new friend join in, then he will get less coffee and there is no way you can share your coffee evenly.
In general, a whole number x divides another whole number y if and only if you can find a whole number n such that
x $\times$ n = y
For example, 24 is easily divisible by 3 because 3 times 8 is equal to 24.
Given below is the divisibility chart.
Divisibility Rules Chart
Divisibility by 2
A number is divisible by 2 if it is an even number.

Example: 295522, 1254, 124, 2984236666 are all divisible by 2.

Divisibility by 3
For the considered number add up all the digits and find its sum. If the sum is divisible by 3 so will be the number.

Example: 12123 (1 + 2 + 1 + 2 + 3 = 9), 9 is divisible by 3. Therefore, 12123 is divisible by 3.

217 (2 + 1 + 7 = 10), 10 is not divisible by 3. Therefore, 217 is not divisible by 3.

Divisibility by 4
For the given number check whether the last two digits in the number are divisible by 4 then so is the number.

Example: 5636, this ends in 36 which is divisible by 4. Therefore, 5636 is divisible by 4.

1719, this ends in 19 which is not divisible by 4. So 1719 is not divisible by 4.

Divisibility by 5
Numbers ending in 5 or 0 are always divisible by 5.
  • If the last digit for the given number is 0 then multiply the remaining digit by 2.
Example: 90 ends in zero considering 9 and multiplying it by 2 we get 18 which is same as dividing 5($\frac{90}{5}$ = 18).
  • If the last digit in the number is 5, multiply the remaining digits by 2 and add one.
Example: 625 ends in 5, considering 62 and multiply it by two and by adding 1 to the result we get 125 which is similar to 5({$\frac{625}{5}$ = 125).

Divisibility by 6
If the Number is divisible by both 2 and 3 then it is divisible by 6.

Example: 114 is divisible by both 2 and 3 as it is even and (1 + 1 + 4 = 6), and 6 is divisible by 3.

164 is not divisible by 6. Though 2 is even but (1 + 6 + 4 = 11) 11 is not divisible by 3.

Divisibility by 7
For the given number double the last digit and subtract it from the rest of the number
If the solution is 0 or it is divisible by 7 then the number is divisible by 7.

Example: 91, double the last digit which is 2, subtracting from 9 we get 7 which is divisible by 7.
198, double the last digit we get 16 and subtracting from 19 we get 3 which is not divisible by 7.

Divisibility by 8
If the last three digits are divisible by 8 then number is divisible by 8.

Example: 215016, last three digits are 016 which is divisible by 8. Therefore, the number is divisible by 8.

12451, last three digits are 451 is not divisible by 8. So 12451 is not divisible by 8.

Divisibility by 9

Add up all the digits for the number and find the sum. If the sum is divisible by 9 then number is divisible by 9.

Example: 43785, (4 + 3 + 7 + 8 + 5 = 27) is divisible by 9, therefore 43785 is too!

2013 (2 + 0 + 1 + 3 = 6) 6 is not divisible by 9 and therefore we cannot divide 2013 by 9.

Divisibility by 10

If the number ends in 0, it is divisible by 10.
Example: 190 -Yes
262 - No