#Maths Fundamentals (Numbers Part 2)- Written by NM Mishra on the behalf of Brilliant Academy of Learning Pvt Ltd on 07/05/2020#

      Rules of Divisibility
1. Divisible by 2 - If last digit of any number is 0,2,4,6,8 that number will be divisible by 2 .
2. Divisible by 3 - If sum of digits of any number be divisible by 3 , that number will be divisible by 3. Ex. - 657
6+5+7 = 18  Here 18 is divisible by 3 , so 657 will be divisible by 3 .
3. Divisible by 4 - If last two digits of any number be divisible by 4 , that number will be divisible by 4 . Ex. - 571136. Here 36 is divisible by 4 , so 571136 will be divisible by 4.
4. Divisible by 5 - If last digit of any number be 0 or 5 that number will be divisible by 5. Ex. - 7320, 97565. Here last digit of 7320 is 0 and last digit of 97565 is 5 , so both numbers will be divisible by 5.
5. Divisible by 6 - If any number be divisible by 2 & 3 both , that number will be divisible by 6. Ex. - 54324 . Here last digit of the number is 4 ,so it will be divisible by 2. The sum of 5+4+3+2+4 =18 , which is divisible by 3. So this number will be divisible by 3. Since 54324 is divisible by both 2 & 3 , so it will be divisible by 6.
6. Divisible by 7 - To find out whether any given number is divisible by 7 or not we will try to understand through following example :
Is 2401 divisible by 7 ?
Firstly take off the last digit of the number and multiply it by 2 and then subtract this from the remaining number. The last digit of the number 2401 is 1 . When we multiply 1 by 2 , we get 2 . Now we have to subtract 2 from remaining part of 2401 that is from 240. When we subtract 2 from 240 we get 238. Now we have to repeat the same process. The last digit of 238 is 8. Now we have to take off 8 from 238. Multiply 8 by 2 , we get 16. Now we have to subtract 16 from remaining part of 238 that is from 23. When we subtract 16 from 23 we get 7 which is multiple of 7. So 2401 is divisible by 7. In this way we can test the divisibility of 7.
7. Divisible by 8 -  If last 3 digits of any number be divisible by 8 , that number will be divisible by 8. Ex. - 753512, 3427128,9856000 . The last 3 digits of numbers are respectively 512,128,000 and these are divisible by 8 , so 753512,3427128 & 9856000 will be divisible by 8.
8. Divisible by 9 -  If sum of digits of any number be divisible by 9 , that number will be divisible by 9. Ex. -  73458 . Here 7+3+4+5+8=27. Since 27 is divisible by 9 , so 73458 will be divisible by 9. 
9. Divisible by 10 - If last digit of the number be 0 , that number will be divisible by 10.
10. Divisible by 11 -  If difference between sum of alternate digits of any number be 0 or multiple of 11 ,that number will be divisible by 11. Ex. - 57387. Here sum of 5+3+7 is 15. The sum of 7+8 is 15. The difference between 15 and 15 is zero. So 57387 will be divisible by 11. Let us take another example like 75218. Here sum of 7+2+8=17 and sum of 5+1 =6 . The difference between 17 and 6 is 11 which is multiple of 11. So 75218 will be divisible by 11.
11. Divisible by 12 - If any number be divisible by 3 and 4 both that number will be divisible by 12.
12. Divisible by 13 -  Subtract the 9 times of last digit from the remaining part of the number . If that is divisible by 13 , then the number will be divisible by 13. Let us find out whether 1521 is divisible by 13 or not.
Multiply last digit of the number that is 1 by 9 . Now the product is 9. Remaining part of 1521 is 152. Subtract 9 from 152. The remainder is 152- 9 =143. Now 143 is divisible by 13 , so 1521 will be divisible by 13.
13. Divisible by 14 - If the number is divisible by 2 and 7 both, that number will be divisible by 14. To test the divisibility by 14 , add last two digits of the number to twice the remaining part of the number. If the sum is divisible by 14 , then that number will be divisible by 14.
14. Divisible by 15 - If the number is divisible by 3 and 5 both , that number will be divisible by 15.

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