NUMBER SYSTEM CHAPTER 3

TEST FOR DIVISIBILITY

DIVISIBLE BY’2’:
             When the last digit of a number is either 0 or even, then the number is divisible by 2.

Example: 26,58,20,46,1256,532656 …………….. etc.

DIVISIBLE BY ‘3’:
       When the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

Example:
 1533      1+5+3+3=12, which is divisible by 3 so 1533 is also divisible by 3.
 126         1+2+6=9,  which is divisible by 3 so 126 is also divisible by 3.
96369     9+6+3+6+9=33, which is divisible by 3 so 96369 is also divisible                                                     by 3

DIVISIBLIE BY ‘4’:
     When the last two digits are divisible by 4 or zeros, it is multiple by 4.

Example:
       6428   last two digits is 28 it is divisible by 4 so the example is also divisible by 4.
       15200 last two digits are 00 so its divisible by 4 the example also divisiblee by 4.

DIVISIBLE BY ‘5’:
       Which number having 0 or 5 at the end of the number its divisible by 5.

Example:
         45,90,8520,6235,695425,60000……….. etc.


DIVISIBLE BY’6’:
          When the number divisible by both 3and 2,then the perticular number is divisible by 6 also.

Example:
      96,720,540,256,…………etc.

DIVISIBLE BY’7’:
           A number is divisible by 7 when the differnce between twice the digit at once place the number formed by other digits is zero or multiple of 7.

Example:
        658= 65-2*8 =49 here the unit place is 8 its multiple by 2 and the difference between the number is 49. So the number is divisible by 7.

DIVISIBLE BY’8’:
       When the last three digits are divisible by 8 or zeros  the number is divisible by 8. Last three or more digits of a number are zero is also divisible by 8.

Example:
          4456 the last three digits are divisible by 8,so the number also divisible by 8.

DIVISIBLE BY’9’:
          The sum of the all digits of a number is divisible by 9,then the number is divisible by 9.

Example:
     936819    9+3+6+8+1+9=36 which is divisible by 9 the number also divisible by 9.
    123456789 1+2+3+4+5+6+7+8+9=45 which is divisible by 9 number also divisible by 9.


DIVISIBLE BY ‘10’:
        When the last number ends with zero the number is divisible by 10.

Example:
   250,63520,369852140,2500,36000,…………… etc.

DIVISIBLE BY’11’:
      When the sum of the digits at odd and even places are equal or differ by 11,then the number also divisible by 11.

Example:
       217382 sum of digits in odd places:2+7+8=17 
                   Sum of digits in even places:1+3+2=6
               The difference is 11. So the number is divisible by 11.

DIVISIBLE BY ‘12’:
            The number which is divisible  by 4 and 3 is also divisible by 12.

Example:
              2244 is divisible by both 3 and 4 so the number is divisible by 12.
              3648 is divisible by both 3 and 4 so the number is divisible by 12.

DIVISIBLE BY ‘125’:
         
A number is divisible by  125 when the number made by last three digits are divisible by 125.

Example:
         5684125  is divisible by 125 as the last three digits of the number is divisible by 125,so the number is divisibnle by 125.
         
         65845250  is divisible by 125 as the last three digits of the number is divisible by 125,so the number is divisibnle by 125.

    BASIC NUMBER THEORY
·         Square of every even number is an even number while squre of odd number is an odd number.

·         A number obtained by squaring a number does nit have 2,3,5,7 or 8 at its unit place.

·         Sum of frist natural numbers =n(n+1)
                                                  2

·         Sum  of frist n odd numbers= n2

·         Sum of frist n even numbers= n(n+1)


·         Sum of square of frist n natural numbers = n(n+1)(2n+1)  
                                                                        6

·         Sum of cubes of frist n natural numbers =[n(n+1)]2
                                                                 2  

·         For any natural number n,(n3-n) is divisible by 6.

·         The product of three consecutive number is always divisible by 6.
 
Arithmetic series:
         
       a,(a+d),(a+2d),(a+3d),………………………
        a= 1st term, d= common differnce.
    Nth term= a+(n-1)d
Sum of n terms = n/2[2a+(n-1)d]
Sum of n terms = n/2 (a+d), where i= last term

Geometric series:

         a,ar,ar2,ar3,………
        a= 1st term r= common ratio,then
         sum of n terms= a(1-rn)/(1-r) where r<1
         sum of n terms = a(1-rn)/(r-1) where r>1
NUMBER SYSTEM CHAPTER 3 NUMBER SYSTEM CHAPTER  3 Reviewed by SSC-IBPS on 14:30:00 Rating: 5

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