7, ఫిబ్రవరి 2015, శనివారం

210/4.- Mallapragada's Mathematics (6th Standared)



1.   Write the greatest 4 digit number and express it in the form of its prime factors.

2.   Find the largest number which is a factor of each of the numbers 504,792 and 1080

3.   The length, breadth and height of a room are 12m,15m and 18 m respectively,  Determine the longest tape which can measure all the three dimensions of the room exactly.

4.   Check whether the following numbers are divisible by 11.

1)   859484, ii) 10824  iii) 20801

5.   Find the smallest number which when added to 5 is exactly divisible by 12,14,and 18.

6.   Find the greatest 3 digit number which when divided by 75,45 and 60  leaves (i) no remainder (ii) the remainder 4 in each case

7.   Three measuring tapes are 64cm, 72 cm and 96 cm. What is the least length that can be measured by any one of the tapes exactly?
8.   Write the nearest number to 1240 which is divisible by 11?

9.   Find the smallest number that must be added to 123, so that it becomes exactly divisible  by 5

10.                      What is the greatest Prime number between 1 and 20?

11.                     Write three pairs of prime numbers less than 20 whose sum is divisible by 5?

12.                     The LCM of two numbers is 290 and their product is 7250, what will be its HCF?

13.                     The product of two numbers is 3276 if their HCF is 6 find their LCM.

14.                     The HCF of two numbers is 6 and their LCM is 36.  If one of the numbers is 12, find the other.

15.                     Find the smallest number that can be subtracted from 1965, so that it becomes divisible by 4?

16.                     Find the HCF of 12,16 and 28 by prime factorization method

17.                     Is 100000 is divisible by 4 ? why?

18.                     Is 9876104 divisible by 8?

19.                     7224 divisible by 6 ? why?

20.                     Write a polyndrome number of six digits. 


                                        





















             
Answers


Om Sri Ram,            Om Sri Ram              Om Sri Ram

1.   Write the greatest 4 digit number and express it in the form of its prime factors.

Ans. The greatest four degit number is “9999”

          3)9999

          3)3333            9999= 3x3x11x101

        11)1111

             --------

              101

             -------



2.   Find the largest number which is a factor of each of the numbers 504,792 and 1080

Ans. Let us find the HCF of 504 and 792

        504)792 (1

                504

              -------

               288 )  504 (1                72)1080(14

                          288                           1008    

                         -------                        ----------

                          216 ) 288 ( 1           72   )  72  ( 1 

                                     216                           72

                                    -------                       ----------

                                       72 ) 216 (3              0

                                               216

                                              -------

 

3.   The length, breadth and height of a room are 12m,15m and 18 m respectively,  Determine the longest tape which can measure all the three dimensions of the room exactly.

Ans. 12 = 2x2 x3   , 15 = 3 x 5     18 = 2 x 3 x 3

          Now H.C.F. = 3



4.   Check whether the  following number are divisible by 11.



1)   859484,

        Ans. 859484 

                The sum of the digits at odd places =4+4+5=13

                 The sum of the digits at even places=8+9+8=25

                 Their difference = 25 – 13 = 12,

                 The difference is not Zero, now not divisible by 11

  

5.   Find the smallest number which when added to 5 is exactly divisible by 12,14,and 18.

Ans. 2)12, 14, 18

         3)06, 07, 09

          ---------------

    2,7,3    L.C.M. 2 x 3x 2x 7x 3= 252

Required smallest number – 252-5 =247

    

6.   Find the greatest 3 digit number which when divided by 75,45 and 60  leaves (i) no remainder (ii) the remainder 4 in each case

Ans. I)   75, 45, 60   L.C. = 5 x3x 5x 3 x4=900

          The required number with no remainder =900

         

        ii) DThe required number with remainder 4 in each

              case = 900 + 4 = 904

  

7.   Three measuring tapes are 64cm, 72 cm and 96 cm. What is the least length that can be measured by any one of the tapes exactly?

2)64, 72, 96

2)32, 36, 48        L.C.M 2x2x2x2x2x2x3x3 = 576 Cm.

2)16, 18, 24

2)08, 09, 12

2)04, 09, 06

2)02, 09, 03

3)02, 03, 01

2)01, 03, 01

3)01, 01, 01



8.   Write the nearest number to 1240 which is divisible by 11?

Ans. 11 x 112 = 1232

          11 x 113= 1243



9.   Find the smallest number that must be added to 123, so that it becomes exactly divisible  by 5

Ans. Then the number becomes 123+2 =125

          Now 5 is devisible.



10.                      What is the greatest Prime number between 1 and 20 ?

Ans.  1 and 20 are 2,3,5,7,11,13,17,19,   The greatest prime

          number is 19



11.                     Write three pairs of prime numbers less than 20 whose sum is divisible by 5?

Ans. (3,7), (7,13),(17,3) The sum of each pair divisible by 5.



12.                     The LCM of two numbers is 290 and their productis 7250, what will be its HCF?

Ans.  290 x HCF = 7250

           HCF = 7250/290 = 25



13.                     The product of two numbers is 3276 if their HCF is 6 find their LCM.

Ans. Product of two numbers = 3276, HCF = 6 LCM= ?

          L.C.M. x H.C.F. = product of two numbers

           L.C.M = 3276/6 =546



14.                     The HCF of two numbers is 6 and their LCM is 36.  If one of the numbers is 12, find the other.

Ans.  HCF.6,LCM.36, one number is 12, 2nd number is “x”

          HCF x LCM = 12 x x   , x= 6x36/12 = 18



15.                     Find the smallest number that can be subtracted from 1965, so that it becomes divisible by 4?

Ans. The last two digits is 65. Subtracted is “1” =64 we know that 1964 is devisible by 4   



16.                     Find the HCF of 12,16 and 28 by prime factorization  method



2)12                              2)16                        2)28

2)06                              2)08                        2)14

3)03                              2)04                        7)07

  ----                               2)02                         -----

   01                              --------                        01

                                         01

12= 2x2x3                 16=2x2x2x2          28=2x2x7

The common factor is 2x2 =4

        

17.                     Is 100000 is divisible by 4 ? why?

Ans. 100000 = 1000 x 100

         Now 100 devisible by 4  i.e. 100000 is devisible by 4



18.                     Is 9876104 divisible by 8?

Ans. Given the number last 3 digits “104” It is devisible by

        8, The given the no. is devisible by 8



19.                     7224 divisible by 6 ? why?

Ans. Units place is 4, it is devisible by 2

         The sum of the degits 7+2+2+4=15

          “15” is multiple of 3 , given number 2 &3 is divisible  

         now 6is divisible.

        

20.                     Write a polyndrome number of six digits.

Ans. The six digited polyndrome number is “ 123321”