Divisibility rules(11)

Divisibility rule of 11:-

 Number=abcdef

                sum of odd places digits=b+d+f.

                sum of even plces digits=a+c+e.

       Differnce of these two =(b+d+f)-(a+c+e)

       should be divisible by 11(0,11,22 ........ ).  

         Ex-8294,

          Sum of odd places digits=4+2=6.

          Sum of even places digits=9+8=17.

      Difference=17-6=11,here difference is divisible by 11,so 8294 is also divisible by 11.

                 

Divisibility rules(7)

1.Divisibility rule of 7:-


       

           161➝16-1×2=14, it is divisible by 7,                 
              so 161 will be divisible by 7.

             273⟶27-3྾2=21 it is divisible by 7,
              so 273 will be divisible by 7.


             581➝58-1×2=56 it is divisible by 7,
              so 581 will be divisible by 7. 



   * Which of following numbers are         divisible by 7.
1. 301  2. 378 3.462  4.4501  5.994



* Fill in the blank with suitable number.

a .23*     so it is divisible by 7.

b.56*9     so it is divisible by 7.

c.32*6    so it is divisible by 7.

d.35425* so it is divisible by 7.

Divisibility rules

  Divisibility (➗)-

1. Divisibility rule of 5: -A number which has a unit place 0 or 5, then the number will be divisible by 5.Ex-125,123450,2375.

Note-Unit place should be 0 or 5.

2.Divisibility rule of 10:- A number is divisible by 10 if unit place is '0'.

Ex:-10,1206780,980,25250.

*Which of following is divisible by 5 and 10 ?
1.2340            2.5235           3.73290        4.9835


*What should be added of the following numbers that it is divisible by 5.
1.22           a.3    b.7   c.9   d.5

2.39            a.6   b.3   c.7    d.1

3.41             a.3   b.5   c.4    d.9

4.77             a.13  b.12  c.2   d.7

5.121            a.4    b.0     c.7   d.1

Divisibility rules of numbers

1. Divisibility rule of 3: -A number whose sum of digits is divisible by 3, then the number will be divisible by 3.                                                                                                                     
Ex:- 123, the sum of digits=1+2+3=6, divisible by 3, then 123 is also divisible by 3.

2. Divisibility rule of 6: -A number is divisible by 2 and 3 both, then the number is also divisible by 6.
Ex-23142 is divisible by 2 and 3, so 23142 is also divisible by 6.
Note-6=2★3, HCF(2,3)=1.

3. Divisibility rule of 9: -A number whose sum of digits is divisible by 9, then the number will be divisible by 9.

Ex:-342, the sum of digits=3+4+2=9, Divisible by 9, then 342 is also divisible by 9.

Divisibility rules of numbers

Divisibility rules-

1. Divisibility rule of 2 -A number whose unit place is divisible by 2 (unit place 0,2,4_6,8) then the number will be divisible by 2.Ex-124, here unit place '4' is divisible by 2 then 124 is also divisible by 2.

2. Divisibility rule of 4 - A number whose last two digits(number formed by unit place and ten place) is divisible by 4 then the number will be divisible by 4.Ex-432, here last two digits '32' is divisible by 4 then 432 is also divisible by 4.

3.Divisibility rule of 8-A number whose last three digits (number formed by unit place, ten place, and hundred place) is divisible by 8 then the number is also divisible by 8.     Ex-3456, here last three digits 456 is divisible by 8 then 3456 is also divisible by 8.

Note:- 2= 2¹→last one digit.

           4=2²→last two digits.

           8=2³→last three digits.

           

Properties of numbers

1. If two digits number and a number obtained by reversing its digits are added then it will be divisible by 11.

     Ex-12+21=33,it is divisible by 11.
     
           45+54=99, it is divisible by 11.

       2. If two digits number and a number obtained by reversing its digits are subtracted then it will be divisible by 9.

      Ex-65-56=9, it is divisible by 9.

           93-39=54, it is divisible by 9.

        3. If two digits number and its sum of digits are subtracted then it will be divisible by 9.
      Ex-13-(1+3)=9, it is divisible by 9.

           29-(2+9)=18, it is divisible by 9.