# Divisibility Rules – Number divisible by 2,3,4,5,6,7,8,9,10,11 or 13

Divisibility Rules are useful when you want to find out if the given big number is exactly divisible or not without actually dividing.
This saves a lot of time which is the need of the hour in any competitive exam. This shortcut is especially handy when you are solving Problems on Ages. We shall find out if a number is divisible by 2,3,4,5,6,7,8,9,10,11,13 using various divisibility rules.

### Divisibility Rules – Number divisible by 2

To check if the given number is exactly divisible by 2 follow the below steps
Step 1: Check if the units digit of the given number is even.
Step 2: If the units digit is even, the given number is exactly divisible by 2.
If not, the given number is not exactly divisible by 2.

Example 1:Is 584 exactly divisible by 2.
Step 1: We see that the units digit (4)is an even number.
Thus, we can say that 584 is exactly divisible by 2.

Example 2: Is 627 exactly divisible by 2.
Step 1: We see that the units digit (7)is an odd number.
Therefore, we can conclude that 627 is not exactly divisible by 2.

### Divisibility Rules – Number divisible by 3

To check if the given number is exactly divisible by 3 follow the below steps
Step 1: Add all the digits in the given number until you arrive at a single number.
Step 2: If the single number arrived is 3, 6, 9, then, the given number is exactly divisible by 3. If not the given number is not exactly divisible by 3.

Example 1: Is 95 exactly divisible by 3.
Adding we get, 9 + 5 = 14
Further adding we get,1 + 4=5
we know that 5 is not exactly divisible by 3.
Thus, we can conclude that 95 is not exactly divisible by 3.

Example 2: Is 63 exactly divisible by 3
Adding we get, 6 + 3=9
We know that 9 is exactly divisible by 3.
Therefore, 63 is exactly divisible by 3.

### Divisibility Rules – Number divisible by 4

To check if the given number is exactly divisible by 4 follow the below steps
Step 1: Check if the last two digits of the given number are divisible by 4.
Step 2: If divisible then, the entire number is divisible by 4.
If not, then the entire number is not divisible by 4.

Example 1: Is 624 divisible by 4?
Step 1: Dividing last 2 digits(24) by 4.
We know that 24 is exactly divisible by 4.
So, we can conclude that the given number 624 is also exactly divisible by 4.

Example 2: Is 514 divisible by 4?
Step 1: Dividing last 2 digits(14) by 4.
We know that 14 is not exactly divisible by 4.
So, we can conclude that the given number 514 is also not exactly divisible by 4.

### Divisibility Rules – Number divisible by 5

To check if the given number is exactly divisible by 5 follow the below steps
Step 1: If the given number ends in 0 or 5 it is exactly divisible by 5.
If not then, the given number is not exactly divisible by 5.

Example 1: Is 1015 divisible by 5?
Step 1: We see that the given number ends in 5
Thus, we can say that 1015 is exactly divisible by 5.

Example 2: Is 5551 divisible by 5?
Step 1: We see that the given number ends in 1
So, we can conclude that 5551 is not exactly divisible by 5.

### Divisibility Rules – Number divisible by 6

To check if the given number is exactly divisible by 6 follow the below steps
Step 1:
Check if the given number is Even number.
Step 2: Find the sum of all the digits of the number until you arrive at a single number.
Step 3: If the single number arrived is 3, 6, 9, then, the given number is exactly divisible by 6. If not the given number is not exactly divisible by 6.

Example 1: Is 846 divisible by 6?
Step
1: We see that the given number is an even number.
Step 2: Add the digits we get, 8 + 4 + 6=18
Again adding we get, 1 + 8= 9
Therefore, the given number 846 is exactly divisible by 6.

Example 2: Is 825 divisible by 6?
Step 1: We see that the given number is an odd number.
Step 2: Add the digits we get,8 + 2 + 5=15
Further adding we get, 1 + 5 =6
Even though the sum of the digits is 6, the given number is not exactly divisible by 6 as the given number is odd number.

### Divisibility Rules – Number divisible by 7

To check if the given number is exactly divisible by 7 follow the below steps
Step 1: Multiply the last digit of the given number by 2.
Step 2: Subtract the result obtained in step 1 from the remaining digits of the given number.
Step 3: If the result obtained in Step 2 is either 0 or a number divisible by 7 then, the given number is exactly divisible by 7. If not then, the given number is not exactly divisible by 7.

Example 1: Is 259 divisible by 7?
Step 1: Multiplying the last digit by 2 we get, 9 X 2=18
Step 2: Subtracting the result we get, 25 – 18= 7
Step 3: We know that 7 is exactly divisible by 7
So we can conclude that 259 is exactly divisible by 7.

Example 2: Is 123 divisible by 7?
Step 1: Multiplying the last digit by 2 we get, 3 X 2=6
Step 2: Subtracting the result we get, 12 – 6= 6
Step 3: We know that 6 is not exactly divisible by 7
Thus, we can say that 123 is not exactly divisible by 7.

### Divisibility Rules – Number divisible by 8

To check if the given number is exactly divisible by 8 follow the below steps
Step 1: Check if the given number is Even number.
Step 2: Check if the last 3 digits of the given number is divisible by 8.
Step 3: If divisible then, it is exactly divisible by 8. If not then, it is not exactly divisible by 8.

Example 1: Is 2016 divisible by 8?
Step 1: We see that the given number is an even number.
Step 2: The last 3 digit that is 016 is exactly divisible by 8.
Step 3: Thus, we can conclude that the given number 2016 is exactly divisible by 8.

Example 2: Is 2124 divisible by 8?
Step 1: We see that the given number is an even number.
Step 2: The last 3 digits that is 124 is not exactly divisible by 8.
Step 3: So, we can say that the given number 2124 is not exactly divisible by 8.

### Divisibility Rules – Number divisible by 9

To check if the given number is exactly divisible by 9 follow the below steps
Step 1: Add all the digits of the number.
Step 2: If the number obtained is 9 or a multiple of 9, then the given number is exactly divisible by 9.
If not then, the given number is not exactly divisible by 9.

Example 1: Is 4513 divisible by 9?
Step 1: Adding the digits in the given number we get, 4+5+1+3=13
Step 2: We know that 13 is not divisible by 9.
Step 3
: Thus, we can say that the given number is not exactly divisible by 9.

Example 2: Is 3555 divisible by 9?
Step 1: Adding the digits in the given number we get, 3+5+5+5=18
Step 2: We know that 18 is exactly divisible by 9.
Step 3: Thus, we can say that the given number is exactly divisible by 9.

### Divisibility Rules – Number divisible by 10

To check if the given number is exactly divisible by 10 follow the below steps
Step 1: If the last digit of the given number is 0 then it is exactly divisible by 10.
Step 2: If not then, the given number is not exactly divisible by 10.

Example 1: Is 5510 divisible by 10?
Step 1: Here, we see that the last digit of the given number is 0.
Thus, we can say that the given number is divisible by 10.

Example 2: Is 6201 divisible by 10?
Step 1: Here, we see that the last digit of the given number is not 0.
Thus, we can say that the given number is not exactly divisible by 10.

### Divisibility Rule of 11

To check if the given number is exactly divisible by 11 follow the below steps
Step 1: Find alternative digits in the given number and make 2 separate groups.
Step 2: Find the sum of the digits within each group.
Step 3: Find the difference between the 2 sums.
Step 4: If the difference in the sums is equal to 0 or 11 or multiple of 11, then the given number is exactly divisible by 11.
If not then, the given number is not exactly divisible by 11.

Example 1: Is 5962 divisible by 11?
Step 1: Finding alternative digits and grouping
we get, 5 and 6 -group A and 9 and 2- group B
Step 2: Finding sum of the digits
we get, Group A- 5+6=11 and Group B- 9+2=11
Step 3: Finding the difference between group A and group B
we get, 11-11=0
Step 4: We see that the difference is 0. Therefore, we can say that the given number 5962 is exactly divisible by 11

Example 2: Is 3431 divisible by 11?
Step 1: Finding alternative digits and grouping
we get, 3 and 3 -group A and 4 and 1- group B
Step 2: Finding sum of the digits
we get, Group A- 3+3=6 and Group B- 4+1=5
Step 3: Finding difference of group A and group B
we get, 6-5=1
Step 4: We see that the difference is not 0 or multiple of 11. Thus, we can say that the given number 3431 is not exactly divisible by 11

### Divisibility Rule of 13

To check if the given number is exactly divisible by 13 follow the below steps Step 1: Find alternative groups of 3 digits from the given number starting from the right. One alternative group to be group A and another alternative group to be Group B.
Step 2: Add the alternative Group A and Group B to arrive at two sums.
Step 3: Find out the difference between the 2 sums.
Step 4: If the difference is equal to 0 or a multiple of 13 then, the given number is exactly divisible by 13.
If not the given number is not exactly divisible by 13.

Example 1: Is 2,456,121,241,514 divisible by 13?
Step 1: Finding alternative groups
We get, Group A- 514,121,2
And Group B- 241,456
Step 2: Adding the alternative Groups
We get, Group A =514+121+2=637
Group B= 241+456=697
Step 3: Finding the difference between the 2 sums.
We get, Group A- Group B- 637-697=60
Step 4: We see that the difference(60) is neither equal to 0 nor a multiple of 13. Thus ,the given number is not exactly divisible by 13.

Example 2: Is 32,903 divisible by 13?
Step 1: Finding alternative groups
We get, Group A-903
And Group B-32
Step 2: Adding alternative Groups.This step can be skipped as there is only 1 number in the group.
We get, Group A=903 and Group B=32
Step 3: Finding the difference between the 2 sums.
We get, Group A- Group B- 903-32=871
Step 4: We see that the difference(871) is a multiple of 13. Thus, the given number is exactly divisible by 13.