how to check if a number is divisible by

Divisibility rules:

How to check if a number is divisible by 2:
the number must ends with an even digit or zero.
For ex: 856,450,968


How to check if a number is divisible by 3:
the sum of digits must by a multiple of 3.
For ex: 5412789
sum of digits =  5 + 4 + 1 + 2 + 7 + 8 + 9 = 36 which is a multiple of 3. Hence 5412789 is divisible by 3.

How to check if a number is divisible by 4:
the last two digits must by divisible by 4
For ex: 57845763424
last two digits 24 is divided by 4. Hency 57845763424 is divisibly by 4.

How to check if a number is divisible by 5:
The last digit must by 0 or 5.
For ex: 5485, 50240 etc.

How to check if a number is divisible by 6:
Number must be even and divisible by 3.
For ex: 36, 222

How to check if a number is divisible by 7:
Subtract the double of last digit from the remaining number. the result must be divisibly by 7.
if the result comes out to be too large to identify that it is divisible by 7. then perform the above operation again on that number. refer the below example.

For ex: 367409
step 1: double of last digit: 9 X 2 = 18
remaining number: 36740
result = 36740-18 = 36722
since the result too is large perform the same operation on 36722. i.e; 3672-4 = 3668 => 366-16 = 350 = > 35 - 0 = 35.
Since 35 is divisible by 7. 367409 is divisible by 7.

How to check if a number is divisible by 8:
the last three digits must by divisible by 8
For ex: 12345120

last three digits 120 is divided by 8. Hence 12345120 is divisibly by 8.

How to check if a number is divisible by 9:
the sum of digits must by a multiple of 9.
For ex: 621124857
sum of digits =  6 + 2 + 1 + 1 + 2 + 4 + 8 + 5 + 7 + 9 = 45 which is a multiple of 9. Hence 621124857 is divisible by 9.

How to check if a number is divisible by 10:
the last digit must be 0.
For ex: 100,240 etc

How to check if a number is divisible by 11:
subtract the sum of even digits from sum of odd digits. the result must be divisible by 11.
For ex: 8162.
sum of odd digits - sum of even digits = divisible by 11

=> 14-3=11 is divisible by 11. Hence 8162 is divisible by 11.

How to check if a number is divisible by 12:
The number must be divisible by both 3 and 4.
For ex: 144, 6984

How to check if a number is divisible by 13:

Add the four times of last digit to the remaining number. the result must be divisibly by 13.
if the result comes out to be too large to identify that it is divisible by 13. then perform the above operation over and over again as required. refer the below example.

For ex: 329732
step 1: four times of the last digit: 2 X 4 = 8
remaining number: 32973
result = 32973 + 8 = 32981
since the result too is large, perform the same operation on 32981. i.e; 3298 + 4 = 3302 => 330  + 8 = 338 = > 33 + 32 = 65 => 6 + 20 = 26.
Since 26 is divisible by 13. 329732 is divisible by 13.

How to check if a number is divisible by 14:
The number must be divisible by both 2 and 7.
For ex: 35602

How to check if a number is divisible by 15:
The number must be divisible by both 3 and 5.
For ex:7860

How to check if a number is divisible by 16:
the last four digits must by divisible by 16
For ex: 20064

last four digits 0064 is divided by 16. Hence 20064 is divisibly by 16.

How to check if a number is divisible by 17:
Subtract the five time of last digit from the remaining number. the result must be divisibly by 17.
if the result comes out to be too large to identify that it is divisible by 17. then perform the above operation over and over again as required. refer the below example.

For ex: 89216
step 1: five times of last digit: 6 X 5 = 30
remaining number: 8921
result = 8921-30 = 8891
since the result too is large, perform the same operation on 8891. i.e; 889-5 = 884 => 88-20 = 68

Since 68 is divisible by 17. 89216 is divisible by 17.

How to check if a number is divisible by 18:
The number must be divisible by both 2 and 9.
For ex: 104112

How to check if a number is divisible by 19:
Add the two times of last digit to the remaining number. the result must be divisibly by 19.
if the result comes out to be too large to identify that it is divisible by 19. then perform the above operation over and over again as required. refer the below example.

For ex: 99655
step 1: two times of the last digit: 5 X 2 = 10
remaining number: 9965
result = 9965 + 10 = 9975
since the result too is large, perform the same operation on 9975. i.e; 997 + 10 = 1007 => 100 + 14 = 114 = > 11 + 8 = 19
Since 19 is divisible by 19. 99655 is divisible by 19.

How to check if a number is divisible by 20:
the last two digits must by divisible by 20
For ex: 1080

last two digits 80 is divided by 20. Hence 1080 is divisibly by 20.

That's it for now. Please leave your suggestions, feedback or tricks in the comments section below.


Hope it helps
Thanks

How to calculate cube root of a number

How to Calculate Cube root of a number between 11 and 100 in your mind.

Cube root of a number can be a very difficult task specially when it lies in the range of 11 and 100. How would you like if you can do it in your head in two seconds in a competitive exam. It will give you an edge over others.

Now, without taking much of your time. Below is the trick.

Things to remember:
A) Cube of numbers from 1 to 10 i.e

1   = 1
2   = 8
3   = 27
4   = 64
5   = 125
6   = 216
7   = 343
8   = 512
9   = 729
10 = 1000

Notice that cube of every number ends with itself except(2,3,7,8).

B) Cube of 2 ends with 8 and vice versa. Cube of 3 ends with 7 and vice versa.

 Main Method():


Lets discuss this with an example.

To find out the cube root of  421875

Solution: Let cube root of this number be AB.

we will first find the B with the help of last three digits

B will be the same as the last digit of the question(here 421875) with an exception that
if last digit is 2, B will be 8
if last digit is 8, B will be 2
if last digit is 3, B will be 7
if last digit is 7, B will be 3

Also, last three digits are ignored as soon as we find B.


here, last digit is 5. so, B is 5.

Now to find A, we are left with only 421.

now, 421 lies between 7(cube 343) and 8(cube 512). so, the minimum of these two will be the A(i.e. 3)


Hence answer is 75.

Another example when last digit is either 2,3,7 or 8.

To find out the cube root of  50653.

To find B, Take last three digits. 653
B will be 7 as the last digit is 3.

To find A, Take remaining digits. 50
50 lies between 3(cube 9) and 4(cube 64). SO, the minimum of these two will be A(i.e. 3)

Hence, the answer is 37.


Thank you,
Hope it helps.