Divisibility rules| Math tricks for Competitive Exams| Easy learning

 

                              Divisibility Rules

 

·        Divisibility rule for 2:

                                    If the unit digit of the given number is even (2,4,6,8) or 0 then the given number is divisible by 2.

Eg.1 Is 238752 divisible by 2?

Solution:

             Unit digit of the given number is 2. So that the number is divisible by 2. 

             238752/2 = 11936

Eg.2 Is 896763 is divisible by 2?

Solution:

              Unit digit of the above-given number is odd. So it is not divisible by 2.

                896763/2= 248381+1 (remainder)

·         Divisibility rule for 3:

                               If the sum of the digits of the given number are divisible by 3, the number will be divisible by 3.

Eg.1 Check if 85203 is divisible by 3 or not?

Solution:

               Sum of the digits = (8+5+2+0+3)

                                              = 18, which is divisible by 3

               Then 85203 also divisible by 3.

Eg.2 check if the number 79154 is divisible by 3 or not?

Solution:

              Sum of the digits = (7+9+1+5+4)

                                              = 26, which is not divisible by 3

Then the given number is not divisible by 3.

·        Divisibility rule for 4:

                                If the last two digits of the given number are divisible by 4, the whole number will be divisible by 4.

Eg.1 Is 97344 divisible by 4?

Solution:

               Last two digits = 44, which is divisible by 4

Then the given number is divisible by 4.

Eg.2 Is 92659 divisible by 4?

Solution:

              Last two digits = 59, which is not divisible by 4

Then the given number is not divisible by 4.

 

·        Divisibility rule for 5:

                            If the unit digits of the given number are 5 or 0. Then it will be divisible by 5.

Eg.1 Is 83975 divisible by 5?

Solution:

              Unit digit = 5

Yes, given the number is divisible by 5

Eg.2 Is 988757 divisible by 5?

Solution:

              Unit digit = 7

No, the given number is not divisible by 5.

·        Divisibility rule for 6:

                         If the number is divisible by both 2 and 3. Then it is also divisible by 6.

Eg.1 Is 846 divisible by 6?

Solution:

             Unit digit = 6 (even number), so the number is divisible by 2

             Sum of digits = (8+4+6)

                                 = 18 (divisible by 3)

Then the given number is divisible by 6.

Eg.2 Is 983 divisible by 6?

Solution:

             Unit digit = 3 which is not divisible by 2

       Sum of digits = (9+8+3)

                             = 19, which is not divisible by 3

So, the given number is not divisible by 6.

·        Divisibility rule for 7:

             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.

Eg.1 Is 9758 divisible by 7?

Solution:

               Multiplying the last digit by 2:

                                     8 X 2 = 16

               Subtracting 16 from remaining digits:

                                     975 – 16 = 959

               Again, multiply the last digit by 2:

                                     9 X 2 = 18

               Subtracting 18 from remaining digits:

                                     95 – 18 = 77, which is divisible by 7

So, the given number is divisible by 7.

Eg.2 Is 1389 divisible by 7?

Solution:

            Multiplying the last digit by 2:

                                           9 X 2 = 18

           Subtracting 18 from the remaining digits:

                                  138 – 18 = 120

           Again, multiplying last digit by 2

                                  0 X 2 = 0

           Subtracting 0 from remaining digits

                                  12 – 0 = 12, which is not divisible by 7.

So, the given number is not divisible by 7.

·        Divisibility rule for 8:

                          If the last three digits of the given number are divisible by 8. Then the number is divisible by 8.

Eg.1: Is 9856 is divisible by 8?

Solution:

             Last three digits = 856

            and   856/8 = 107 

So, the given number is divisible by 8.

Eg.2: IS 57833 divisible by 8?

Solution:

             Last three digits = 833

             and 833/8 = 104 + 1(remainder) 

So, the given number is not divisible by 8.

·        Divisibility rule for 9:

                           If the sum of all digits of the given number is divisible by 9, then the number is divisible by 9.

Eg.1: Is 3555 divisible by 9?

Solution:

             Sum of digits = 3+5+5+5

                                    = 18, which is divisible by 9

So, 3555 is divisible by 9.

Eg.2: Is 4513 divisible by 9?

Solution:

            Sum of digits = 4+5+1+3

                                  = 13, which is not divisible by 9

So, 4513 is not divisible by 9.

·        Divisibility rule for 10

                           If the unit digit of the number is 0, then the number is divisible by 10.

Eg. 1 Is 4750 divisible by 10?

Solution:

              Unit digit = 0

Then 4750 is divisible by 10.

Eg.2: Is 5985 divisible by 10?                    

Solution:

             Unit digit = 5, which is not 0

So, 5985 is not divisible by 10.

·        Divisibility rule for 11:

                            Step 1: Add the odd digits of the given number

                            Step 2: Add the even digits of the given number

                            Step 3: Subtract step 2 from step 1.

                        Step 4: If the result got in Step 3 is divisible by 11. The given number is also divisible by 11.

Eg.1: Is 53856 divisible by 11?

Solution:

             Sum of odd digits = 5+8+6 = 19

            Sum of even digits = 3+5 = 8

            Subtracting even digits from odd digits:

                                   = 19 – 8

                                   = 11, which is divisible by 11

          So, the given number is divisible by 11.

          Eg.2: Is 37843 divisible by 11?

          Solution:

             Sum of odd digits = 3+8+3 = 14

             Sum of even digits = 7+4 = 11

             Subtracting even digits from odd digits:

                                   = 14 – 11

                                   = 3, which is not divisible by 11

         So, the given number is not divisible by 11.

·        Divisibility rule for 13:

                          Step 1: Multiply the unit digit of the given number by 4.

                          Step 2: Add the product received in step 1 to the remaining number.

                          Step 3: If the result got in step 2 is divisible by 13, the given number is also divisible by 13.

Eg.1: Is 3978 divisible by 13?

Solution:

            Multiplying unit digit by 4:

                           = 8 X 4 = 32

            Adding the product in remaining number:

                           = 397 + 32

                           = 429

            Again, multiplying unit digit by:

                           = 9 X 4 = 36

             Adding the product in remaining number:

                           = 42 + 36

                           = 78, which is divisible by 13.

So, the given number is divisible by 13.

Eg.2 Is 647 divisible by 13?

Solution:

             Multiplying unit digit by 4 = 7 X 4

                                                      = 28

             Subtracting product from the remaining number

                                                      = 64 – 28

                                                      = 36, which is not divisible by 13.

So, the given number is not divisible by 13.