Divisibility Rules Which Are Useful For Competitive Exams

DIVISIBILITY TEST

Each number has its own properties by this u can decide that is any number divisible by that prime number or not. Let’s see some of those numbers which can help us in speed math.

1. Divisibility test for 2:

If any number has its last digit divisible by 2, then the number itself is divisible by 2.

2.    Divisibility test for 3:

If sum of all digits of any number is divisible by 3, then number itself is divisible by 3

For example: take 359856. Take some of all digits 3+5+9+8+5+6 =36 here    36 is divided by 3 so that 359856 is divisible by 3

3.     Divisibility test for 4:

If any number has its last two digits are divisible by 4 then number its self is divisible by 4.

For example: Take 78542. In this figure, last two digits are 42 which is divisible by 4, so 78542 is also divisible by 4. But 582522 is not divisible by 4 because its last two digits are not divisible by 4

4.     Divisibility test for 5:

If the number has its last digit is zero or Five then it is divisible by 5. For example, 4825 or 5824250 or 68255 or 242005 or 2512557890 all are divisible by 5

5.     Divisibility test for 6:

6 is a composite number. 6 can be represented as 3*2. So any number is said to be divisible by 6 if it is divisible by both 3 & 2

Same in case of all composite number like 12 = 4*3, 15 =5*3, so in case of

Check divisibility of 4 & 3 and in case of 15 checks for 5 & 3

6.     Divisibility test of 7:

If any number has 4 or more digits then its divisibility by 7 can be tested as:

First, make the group of each three digits and then take the sum of alternative groups. After taking some subtract last two number, u get by summation and if an answer is zero or divisible by 7 next number itself is divisible by 7.

And If a reply is in 3 digits then take the last number, multiply it with 2 and subtract answer from first two digits. If final answer is zero or  divisible by 7 then number itself is divisible by 7

For Example: Take a digit 47582417553556. Here to make the group of 3 numbers we can write this number as  047582417543556. Now a group of 3 numbers is 047 582 417 543 556. Take some of the alternative groups

047+417+556 =1020 & 582+543 = 1125. Now take subtraction 1135-1020=105. Here 105 is divisible by 7, so 47582417553556 is divisible by 7.

If u want to check it for 105. So take the last digit and multiply it with 2 and subtract answer from first two digits. so 5*2 = 10 & first two digits 10 – 10 =0 so 105 is divisible by 7.

7.     Divisibility test for 8:

If any number has its last three digits which are divisible by 8 next number itself is also divisible by 8. For Example, take number 282482545824832. Here last three digits are 832 which is divisible by 8, so number itself is also divisible by 8.

8.     Divisibility test for 9:

If any number is divisible by 9, then the summation of all of its digits are divisible by 9. For Example 1864258452. Take summation of all numbers 1+8+6+4+2+5+8+4+5+2=45. 45 is divisible by 9, so number 1864258452 itself is also divisible by 9.

9.     Divisibility test for 11:

If u want to find divisibility of any number by 11 then first take alternative digits of a number and take summation of these digits then subtract this two number which we have got by summation of alternative numbers. If the final answer is zero or divisible by 11, then the number itself is also divisible by 11.

For Example: take number 6984659. Take summation of alternative number 6+8+6+9=29 & 9+4+5=18 do 29-18=11.

10.    Divisibility test for 13:

Divisibility test for 13 is as same as 7, but a difference is only that final answer should be zero or divisible by 13 if a number is divisible by 13.