8th Class Mathematics Playing with Numbers

Divisibility

Conditions

Example

2.

The last digit is 0 or an even number

9340    0 (Last digit 0)

3456   6 (Last digit is an even number)

\[\therefore \]9340 & 3456 are divisible by 2.

3.

The sum of all the digits of the number is divisible by 3.

4746 (4+7+4++6)+3

=21+\[\div \]3=7

\[\therefore \]4746 is divisible by 3

4.

The number formed by last two digits of the number is divisible by 4 or are 00.

616    16 \[\div \] 4 = 4

8900    00 (Last two digits are 00)

\[\therefore \]616 and 8900 are divisible by 4.

5

The last digit of the number is 0 or 5.

60415   5 (Last digit is 5)

76290  0 (Last digit is 0)

\[\therefore \]60415 and 76 290 are divisible by 5.

6.

The last digit is 0 or an even number, and the sum of all the digits of the by 6.

7596    (7+5+9+6)-3

= 27 - 3 = 9

\[\therefore \]7596 is divisible by 6.

7.

The difference between the number formed by the

digit/digits in front and the doubled value of the last digit is 0 (or) is divisible        

406     406 is divisible by 7 because

 40 - (6 x 2) = 28

28 is divisible by 7.

\[\therefore \]406 is divisible by 7.

8722 is divisible by 7 because

872 -(2x2)= 868

868 is divisible by 7.

\[\therefore \]8722 is divisible by 7.

815      815 is not divisible by 7 because

81 - (5 x 2) = 71

71 is not divisible by 7.

\[\therefore \]815 is not divisible by 7.

8.

The number formed by the last three digits of the number is divisible by 8.                 

3568   568 \[\div \] 8 = 71

\[\therefore \]3568 is divisible by 8.

9.

The sum of all the digits of the number is divisible by 9.

6048    (6+0+4+8)-9= 18-9=2

\[\therefore \]6 048 is divisible by 9.

10.

The last digit is 0.

9310    0 (Last digit is 0)

\[\therefore \]9 310 is divisible by 10.

11.

The difference of the sum of the digits in even places    and the sum of the digits   in odd places is 0 or is divisible by 11.                  

1364    ((3 + 4) - (1 + 6)) = 0

3729    ((7 + 9) - (3 + 2)) = 11

\[\therefore \]1364 and 3 729 are divisible by 11.

25176   ((5 + 7) - (2 + 1 + 6)) = 3

\[\therefore \]25176 is not divisible by 11.

12.

The number is divisible by both 3 and 4.                      

648     (6 + 4 + 8 = 18 and  also 48 \[\div \]4=12)

\[\therefore \]648 is divisible by 12.

916    (9+1+6= 16 and

16\[\div \]4=4

\[\therefore \]916 is not divisible by 12 as it is not divisible by 3.