www.rsmaths99.com

CLASS 6 MATHS RS AGGARWL

Contents

1.     Number system  1A, 1B, 1C, 1D, 1E, 1F, 1G

2.  Factors multiples 2A, 2C, 2D, 2E,

EXERCISE – 1A

Q1.   Write the numerals for each of the following numbers:

            I]   Nine thousand eighteen   - 9018

            Ii]   Fifty-four thousand seventy –three - 54073

            Iii]  Three lakh two thousand five hundred six - 302506

            Iv]  Twenty lakh ten thousand eight -  2010008

            V]  six crore five lakh fifty – seven - 60500057

            Vi]  two crore two lakh two thousand two hundred two - 20202202

            Vii]  twelve crore twelve lakh twelve thousand twelve - 121212012

            Viii]  Fifteen crore fifty lakh twenty thousand sixty-eight - 155020068

Q2.      Write each of the following numbers in words:

            I]         63,005 – sixty- three thousand five

            Ii]        7,07,075 – Seven lakh seven thousand seventy-five

            Iii]       34,20,019  - Thirty-four  lakh twenty thousand nineteen

            Iv]       3,05,09, 012 – Three crore five lakh nine thousand twelve

            V]          5,10,03,604 – five crore ten lakhs three thousand six hundred four

            Vi]        Six crore eighteen lakh five thousand eight

            Vii]   Nineteen  crore nine lakh nine thousand nine hundred

            Viii]  Six crore fifteen lakh thirty thousand eight hundred seven

            Ix]  Six crore sixty lakh sixty thousand sixty

Q3.      I]  15768 = (1 x 10000) + (5 x 1000)+ (7 x 100) + (6 x 10) + (8 x 1)

            Ii]  308927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)

            Iii]  2405609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) +(9 x 1)

            Iv]  53618493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000)

       + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)

            V]  60606006 = (6 x 10000000)+ (6 x 1000000)+ (6 x 1000)+ (6 x 1).

Vi]  91010510 = (9 x 10000000)+ (1 x 1000000) + (1 x 10000)

        + (5 x 100)+(1 x 10)

Q4.      I]  62584  ii]  581623   iii]   20507905   iv]  3406507

Q5.      79520986

The place value of 9 at the 90 lakh place = 9000000.

            The place value of 9 at the hundred place = 900

            Hence, the required difference = (9000000 - 900)=  8999100.

Q6.      27650934

            The place value of 7 at the  70 lakh place = 7000000.

            The face value of 7 = 7

            Hence, the required difference = 7000000 – 7 = 6999993.

Q7.      The largest 6-digit nos. = 999999

            The smallest 6-digit nos. = 100000

            Number of all 6-digit nos. = (999999 – 100000) + 1

= 899.999 + 1 = 900,000.    www. rsmaths99.com

Q8.      The largest 7-digit nos. = 9999999

            The smallest 7-digit nos. = 1000000

            Number of all 7-digit nos. = (9999999 – 1000000) + 1

= 8999999 + 1 = 9000000.

Q9.      100 thousands make a lakh.

Q10.   10000 thousands make a crore.

Q11.   837 - 738  = 99.

Q12.   9547999 + 1 = 9548000.

Q13.   9900000 – 1 = 9899999.

Q13.   10000000 – 1 = 9999999.

Q15.   234, 243, 324, 342, 423, 432

Q16.   10357.

Q17.   964320.

Q18.  

 

MILLION

THOUSANDS

HUNDREDS

 

HM

TM

MILLON

HTh

TTh

Th

H

TENS

ONES

I

 

 

 

7

3

5

8

2

1

Ii

 

 

6

0

5

7

8

9

4

Iii

 

5

6

9

4

3

8

2

1

Iv

 

3

7

5

0

2

0

9

3

V

 

8

9

3

5

0

0

6

4

Vi

 

9

0

7

0

3

0

0

6

 

 

C

TL

L

TTh

Th

H

T

O

  

I]  735.821 – seven hundred thirty-five thousand eight hundred twenty-one.

Ii]  6,057,894 – six million fifty-seven thousand eight hundred ninety-four.

Iii]  56,943,821 – fifty-six million nine hundred forty-three thousand eight hundred  twenty-one.

Iv]  37,502,093 –  Thirty-seven million five hundred two thousand ninety-three.

V]  89,350,064 – eighty-nine million three hundred fifty thousand sixty-four.

Vi] 90,703,006 -  ninety million seven hundred three thousand and six.

Q19.                                     www. rsmaths99.com

 

MILLION

THOUSANDS

HUNDREDS

 

HM

TM

MILLON

HTh

TTh

Th

H

TENS

ONES

I

 

3

0

1

0

5

0

6

3

Ii

 

5

2

2

0

5

0

0

6

Iii

 

 

5

0

0

5

0

0

5

 

EXERCISE – 1B COMPARISON OF NUMBERS

Q1.      1003467 > 987965   [ 7 digit number is > 6 digit number ]

Q2.      3572014 <10235401   [ 7- digit < 8 digit number ]

Q3.      325490 < 3260152

Q4.      10357690 < 11243567            [ 0 < 1 ]

Q5.      27596381 > 7965412

Q6.      47893501 < 47894021   [ 3 < 4 ]

Q7.      102345680 > 63521047 > 63514759 > 7355014 > 7354206

Q8.      23794206 > 23756819 > 5032790 > 5032786 > 987876

Q9.      16060666 > 16007777 > 1808090 > 1808088 > 190909 > 181888

Q10.    1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988

Q11.    990357 < 9873426 < 9874012 < 24615019 < 24620010

Q12.    5694437 < 5695440 < 56943201 < 56943300 < 56944000

Q13.    700087 < 8014257 < 8014306 < 8015032 < 10012458

Q14.    893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403

EXERCISE – 1C WORD PROBLEMS ON NUMBER OPERATIONS

Q1.      Total no of person visited the shrine during last two years-

           

                        13 7 8 9 5 0 9

            +          12 9 7 6 4 9 8

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

                           2 6 7 6 6 0 0 7

            ------------------------------------    Ans.

 

Q2.      Sugar produced by all three factories during last yr :-

                        2 4 8 0 9 5 6 5

            +          1 8 7 3 8 5 7 6

                            9 5 6 4 5 6 8

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

                        5 3 1 1 2 7 0 9

            ------------------------------------------ Ans.

 

Q3.      The new number will be  :-

                        3 7 6 8 4 9 5 5

            +             3 6 1 5 0 4 5

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

                        4 1 3 0 0 0 0 0

                --------------------------------- Ans.

 

Q4.        Total no of votes received =   6 8 7 9 0 5     

                                                                                4 9 5 0 8 6

                                                                +                 9 3 7 5 6

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

                                                                                1 2 7 6 7 4 7

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

                Number of invalid votes = 13849

                No. of persons who did not vote = 25467

                 Total no. of registered voters = 1276747 + 13849 + 25467 = 1316063 Ans.

 

 

Q5.         People have primary education =            1 6 2 3 5 4 6

                                    Secondary      “              =             9 7 6 8 6 7 8

                                    Higher              “              =             6 8 3 7 9 5 4

                                    Illiterate          “              =             2 6 8 4 5 3 6

                                Children below age        =                6  9 8 7 8 1

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

                                                                                            2 1 6 1 3 4 9 5                                                                                                                                                     ----------------------------------

                Hence, the total population of state  =  2 1 6 1 3 4 9 5.

                                                               

               

Q6.         Bicycle prod. In a year                     =           8 7 6 5 4 3 5

                Increased prod.                                                   =          1 3 7 8 6 9 8    

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

                No. of bicycle prod. In 2nd yr                      1 0 1 4 4 1 2 4

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

               

No. of bicycle produced in these two years =    8 7 6 5 4 3 5

                                                                                                +      1 0 1  4 4 1 2 4

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

                                                                                                        1 8 9 0 9 5 5 9      Ans.

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

               

Q7.         Sale in a year                    Rs.  2 0 9 5 6 4 8 0

                Sale increased by             Rs.     6 7 0 9 5 7 0

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

                                                                         2 7 6 6 6 0 5 0

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

                Hence, total sale of company during these two years =   Rs. 2 0 9 5 6 4 8 0

                                                                                                                                        2 7 6 6 6 0 5 0

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

                                                                                                                                      4 8 6 2 2 5 3 0   Ans.

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

Q8.         Total population of a city    =      2 8 7 5 6 3 0 4

                                                                (-)          1 6 9 8 7 0 5 9

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

                                                                                1 1 7 6 9 2 4 5

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

                Hence, no, of femals I city = 1 1 7 6 9 2 4 5.

 

Q9.                         1 3 2 4 6 5 1 0

                          (-)   4 6 5 8 6 4 2

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

                                   8 5 8 7 8 6 8                 hence, it is larger by  8 5 8 7 8 6 8

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

 

Q10.                       1 0 0 0 0 0 0 0

                          (-)     5 6 4 3 8 7 9

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

                                4 3  5  6 1 2  1      

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

Q11.       Let the required no. be y. Then 1 1 0 1 0 1 0 1  - y = 2 6 3 5 9 6 7 .

                   y = 1 1 0 1 0 1 0 1  -      2 6 3 5 9 6 7 = 8 3 7 4 1 3 4 .

 

Q12.       ATQ,  y + 89 6 7 5 1 9  = 1 0 7 5 0 3 0 8 .

                Hence, y = 1 0 7 5 0 3 0 8 - 89 6 7 5 1 9   = 1 7 8 2 7 8 9 .

 

Q13.       Total amount    Rs.   2 0 0 0 0 0 0 0

                Spent              (-)         1 3 6 0 7 0 8 5

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

                Money left         =         6 3 9 2 9 1 5

                                                --------------------------   www. rsmaths99.com

 

Q14.       Cost of property = 1 8 5 3 6 0 0 0

                Total collection :      membership fee  =                 7 2 5 3 8 4 0

                                                                Loan                =   5 6 7 5 4 5 0

                                                                Donation        =   2 9 3 7 6 8 0

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

                                                                                             1 5 8 6 6 9 7 0

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

                Amount short by    1 8 5 3 6 0 0 0 - 1 5 8 6 6 9 7 0 = 2 6 6 9 0 3 0 .

 

Q15.       Total amount                     Rs.          1 0 6 7 2 5 4 0

                Amount gave to wife     Rs. (-)        4 8 3 6 9 8 0

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

                Money left                         Rs.             5 8 3 5 5 6  0

                Money gave to son         Rs. (-)        3 9 6 4 7 9 0

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

                Money left                         Rs.              1 8 7 0 7 7 0

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

                Hence,  Rs  1 8 7 0 7 7 0  was received by the daughter.

 

Q16.       Cost  of one chair =    Rs.   1 4 8  5

                Cost of  469 “         =         x      4 6 9

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

                                                                 1 3 3 6 5

                                                 8 9 1 0 x

                                                             5 9 4 0 x x

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

                                                                6 9 6 4 6 5

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

Hence, the cost of chair = Rs. 6 9 6 4 6 5.

 

 

Q17.       Total no. of students          =         1 7 8 6

                Each students contribute  = Rs.     6 2 5

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

                                                                                8 9 3 0

                                                                           3 5 7 2 x    

                                                                     1 0 7 1 6 x x                                                                                                    

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

                                                                      1 1 1 6 2 5 0

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

Hence , total collection   = Rs.  1 1 1 6 2 5 0 .

 

 

Q18.       Screw produce in one day           =              6 9  8 5

                “              “              “   365 “                =        x       3 5 8

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

                                                                                                5 5 8 8 0

                                                                                           3 4 9 2 5 x 

                                                                                       2 0 9 5 5 x x

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

                                                                                        2 5 0 0 6 3 0

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

Q19.   Mr. Bhasker save saves Rs. 8756 in one month.

            Then in 12 month he saves =   8 7 5 6 x 12 = Rs. 105072.

            Hence, in 13 years he saves = Rs. 105072 x 13 = Rs. 1365936.

 

Q20.     Cost of one scooter    = Rs. 36725.

                   Cost of 487 scooter   = Rs. 36725  x  487  =  Rs.  17885075.

 

 

Q21.     In 1 hr aero plane covers     1485 km.

                  In 72 hrs “         “             1485 x 72 = 106920 km.

 

Q22.     Let the one no. be y. Then,     y x 364 = 13421408.

               

Y =   = 36872.

Q23.     Cost of 36 flat = Rs. 68251500. Then cost of each flat  =  

 =                =   

 

Q24.       Gas contained in cylinder = (30250 – 14480)g = 15770g   = 15kg 770g.  [1kg = 1000g]

 

Q25.       Length of cloth = 5 m = 500 cm.  & piece of length = 2m 85 cm = 285 cm. [1m = 100cm]

                  length of the remaining piece = (500 – 285)cm = 215 cm = 2m 15 cm. 

                               

Q26.       For one shirt required length of cloth = 2m 75cm = 275 cm.

                 For  16    “        “              “              “         =  275 cm 44m.

 

 

Q27.       Required cloth for each trouser = 185 cm = 1m 85cm.

 

Q28.     Mass of a brick = 2kg750g = 2000g + 750g =2750g.

                Mass of 14 bricks = 2750 x 14 = 38500 g = 38kg 500g.

 

Q29.     Mass of 8 packets = 10kg 600g = 10600g.

                Mass of each packet =    = 1325 g = 1kg 325 g.

 

Q30.     Length of each piece of rope =

------------------------------------------------------------X-----------------------------------------------------------------

 

EXERCISE -1D  ESTIMATION

 

Q1.        Estimate each sum to the nearest ten:

 

(57 + 34) 

                57 estimated to the nearest ten =  60

                34 estimated to the nearest ten =  30

                Hence, the required estimation = 60 + 30 = 90.

 

Q2.        (95 + 58)

                95 estimated to the nearest ten =  100

                58 estimated to the nearest ten =  60

                Hence, the required estimation = 100 + 60 = 160.

 

Q7.        (356 + 275)        www. rsmaths99.com

                356 estimated to the nearest ten =  360

                275 estimated to the nearest ten =  280

                Hence, the required estimation =360 + 280 = 640.

 

Q10.     Estimate each sum to the nearest hundred

 

(236 + 689)

                236 estimated to the nearest hundred= 200

                689 estimated to the nearest hundred =  700

                Hence, the required estimation = 200 + 700 = 900.

 

Q13.     (3280 + 4395)

                3280 estimated to the nearest hundred= 3300

                4395estimated to the nearest hundred =  4400

                Hence, the required estimation =  3300 + 4400 = 7700.

Q15.     (10083 + 29380)

                10083 estimated to the nearest hundred= 10100

                29380 estimated to the nearest hundred =  29400

                Hence, the required estimation = 10000 + 29300 = 39500.

 

Q16.     Estimate each sum to the nearest thousand:

(32836 + 16466)

                32836 estimated to the nearest thousand  = 33000

                16466 estimated to the nearest thousand  =  16000

                Hence, the required estimation =33000

Q17.     (46703 + 11375)

                46703 estimated to the nearest thousand  = 47000

                11375 estimated to the nearest thousand  =  11000

                Hence, the required estimation = 47000 + 11000 = 58000.

 

Q18.     54 balls in box A = estimated  balls= 50.

                79 balls in box B = estimated balls = 80.

Total no of balls = 50 + 80 = 130.

 

Q19.     Estimate each difference to the nearest ten:

(53 - 18)

                53 estimated to the nearest ten =  50

                18 estimated to the nearest ten =  20

                Hence, the required estimation = 50 - 20 = 30

 

               

Q22.     Estimate each difference to the nearest hundred:


                (678 - 215)     www. rsmaths99.com

                678  estimated to the nearest hundred= 700

                215  estimated to the nearest hundred =  200

                Hence, the required estimation = 700 -  200 = 500.

Q25.     (5612 - 3095)

                5612  estimated to the nearest hundred= 5600

                3095  estimated to the nearest hundred =  3100

                Hence, the required estimation = 5600 – 3100 = 2500.

 

Q26.     Estimate each difference to the nearest thousand

(35863 - 27677)

35863 estimated to the nearest thousand  = 36000

                27677 estimated to the nearest thousand  =  28000

Hence, the required estimation = 36000 – 28000 = 8000.

 

Q27.     47000 – 39000 = 8000.

----------------------------------------------------------------X--------------------------------------------------------------

EXERCISE -1E  ESTIMATING THE PRODUCTS

 

                Estimate each of the products by rounding off each number to the nearest ten.

 

Q1.        38 x 63                                              

                38 estimated to the nearest ten =  40

                63 estimated to the nearest ten =  60

                Hence, the required estimation = 40 x 60 = 2400.

 

Q2.        54 x 47

                54 estimated to the nearest ten =  50     www. rsmaths99.com

                47 estimated to the nearest ten =  50

                Hence, the required estimation = 50 x 50 = 2500.

               

                Estimate each of the products by rounding off each number to the nearest hundred.

 

Q7.        376 x 123

                376 estimated to the nearest hundred= 400

                123  estimated to the nearest hundred =  100

                Hence, the required estimation        = 400 x 100 = 40000.

 

                Estimate each of the products by rounding off the first no. upwards and the second no. downwards :

               

Q13       183 x 154

                183 estimated upwards = 200

                154  estimated downwards = 100

                Hence, the estimated product = 200 x 100 = 20000.

 

Q17.     680 x 164

                680 estimated upwards = 700

                164  estimated downwards = 100

                Hence, the estimated product = 700 x 100 = 70000.

               

Estimate each of the products by rounding off the first no. downwards

and the second no. upwards :     www. rsmaths99.com

 

Q19.     356 x 278

                356 estimated downwards = 300

                278  estimated upwards  = 300

                Hence, the estimated product = 300 x 300 = 90000.

--------------------------------------------------------------X----------------------------------------------------------------------

EXERCISE -1F ESTIMATING THE QUOTIENTS

 

Find the estimated quotient for each of the following :

 

Q1.        87 28              

                87 28               is approximately equal to  90  30 = 3.

 

Q2.        83  17   is approximately equal to  80  20 = 4.

Q8.        729  29  is approx. equal to  700  = 23.33 = 23

Q10.     868   is approx. equal to  900  40 =22.5 = 23 .

----------------------------------------------------X------------------------------------------------------------------

EXERCISE -1G  ROMAN NUMBERS

Roman numbers

I

V

X

L

C

D

M

Hindu-Arabic numerals

1

5

10

50

100

500

1000

 

Q1.         I] 2 = II    II] 8 = VIII           III] 14 = XIV         IV]  29 = XXIX     VIII] 61 = LXI  XI]  91 = XCI

XIV]  105 =  100 + 5 = CV   XV]  114 = 100 + 10 + 4 = CXIV.

Q2.         I] 164 = 100 + 60 + 4 = CLXIV.       III]  226 = 200 +20 + 6 = CCXXVI

                VI]  596 = 500 + 90 + 6 = DXCVI    VIII]  759 = 700 + 50 + 9 = DCCLIX

Q3.         I]   XXVII = 10 + 10+ 7 = 27.            II] XXXIV = 34     IV] LIV = 50 + 4 = 54.

                IX]  CLIV = 100 + 50 + 4 = 154        XII] CDXIV = (500 – 100)+10+4 = 414.

                XIII] CDLXIV = 500 – 100 + 50 + 10 + 4 = 464. XV]  DCCLXVI = 766.

1=I

2 = II

3 = III

4 = IV

5 = V

6 = VI

7 = VII 

8 = VIII

9 = IX

10 = X

11 = XI

12 = XII

13 =XIII

14= XIV

15= XV

16 = XVI

17 = XVII

18 = XVIII

19 = XIX

20 = XX

21 = XXI

22 = XXII

23 = XXIII

24 = XXIV

25 = XXV

26 = XXVI

27 = XXVII

28 = XXVIII

29 =XXIX

30 = XXX

31 =XXXI

32 = XXXII

33 = XXXIII

 34 = XXXIV

XXXV

XXXVI

XXXVII

XXXVIII

XXXIX

40 = XL

41 = XL

42 = XLII

43 = XLIII

44 = XLIV

45 = XLV

46 = XLVI

47 = XLVII

48 = XLVIII

49 = XLIX

50 = L

91= XCI

92 = XCII

93 = XCIII

94 = XCIV

95 = XCV

96 = XCVI

97 = XCVII

98 = XCVIII

99 = XCIX

100 = C

               

------------------------------------------------------------x-------------------------------------------------------------------

EXERCISE – 2A  FACTORS AND MULTIPLES

Even numbers : all multiples of 2 are called even numbers.

Ex. – 2, 4, 6, 8, 10,…..etc

  Odd numbers : numbers which are not multiple of 2 .

Ex.-  1, 3, 5, 7, 9, 11, 13, …etc.

Prime numbers : A number which is divisible by 1 and itself. 

(25 prime nos.1 -100).       www. rsmaths99.com

Ex.- 2, 3 ,5, 7, 11, 13,17, 19, 23,29, 31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 etc.

Composite number : number having more than two factors.

Ex.- 4, 6, 8, 9, 10, 12, 14,  etc.

Natural numbers : counting numbers are called natural numbers.

Ex.- 1, 2, 3, 4, 5, 6, 7, 8, ….etc.

Whole numbers :  All natural numbers together with 0(zero) .

Ex.- 0, 1, 2, 3, 4, 5, 6, 7, 8, ….etc.

               

Q1.      Define :

            [i]   Factor : -A factor of a number is an exact divisor of that number.

            Ex. 20 = 1, 2, 4, 5, 10, 20.

            [ii]   Multiple : A number is said to be a multiple of any of its factors.

            Ex.    20 is a multiple of  the numbers 1, 2, 4, 5, 10 and 20.

Q2.        Factors :-

                [i] 20 = 1, 2, 4, 5, 10, 20.         [ii]  36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.

                [iii]  60 = 1, 2, 3, 4, 6, 10, 12, 15, 20, 30, 60.   [iv]  75 = 1, 3, 5, 15, 25, 75.

Q3.        Multiples:

                [i] 17 = 17, 34, 51, 68, 85       [ii]  23 =  23, 46, 69, 92, 115

                [iii]  65 = 65, 130, 195, 260, 325   [iv]  70 =  70, 140, 210, 280, 350.

Q4.        Even  numbers –[ i]32              [ iii]50                  iv] 58                 [vi]  144

                Odd numbers -   [ii] 37             [ v]69    [vii] 321          [viii] 253.

Q5.      Prime numbers : A number which is divisible by 1 and itself is called Prime numbers.

Ex.- 2, 3 ,5, 7, 11, 13,17, 19, 23,29.

Q7.         I]   Smallest prime number is 2. Ii] even prime no. is 2.

                Iii]  smallest odd prime no. is 3.

Q8.         Ii]  89

Q9.         90, 91, 92, 93, 94, 95, 96,

Q10.       I] no,     ii] 1        iii]  4, 9, 25, 49.   www. rsmaths99.com

Q11.   Composite number : number having more than two factors are called Composite number.

Ex.- 4, 6, 8, 9, 10, 12, 14,  etc.   yes, 9.

Q12.   Twin primes : two consecutive odd prime numbers are known as twin primes.

            Twin primes between 50 and 100.  (59, 61),  (71, 73).

Q13.   Two numbers are said to be co-primes if they do not have a common factor other than 1.

            Ex.- i] 2, 3      ii] 3, 4 iii] 4,5 iv] 4, 9            v] 8, 15.

                Two co-prime need not be prime no. ex. 6, 7 are co-primes, while 6 is not a prime no.

Q14.       I] 36 = 7 + 29       ii] 42 = 5 = 37      iii] 84 = 17 = 67 iv] 98 = 79 + 19.

Q15.       I] 31 = 5 + 7 + 19 ii] 35 = 5 + 7 + 23   iii] 49 = 3+ 5+ 41  iv]   63 = 7 + 13 + 43

Q16.       I] 36 =17 + 19  ii] 84 = 41 + 43       iii] 120 =  59 + 61               iv ] 144 = 71 + 73

Q17.       I]  F         ii] F        iii] F       iv] F

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EXERCISE – 2C

Q1.        We use the division method as shown below:

                 

                12 = 2 x 2 x 3   = 22  x 3

Q2.      We use the division method as shown below:

           

                   18 =  2 x 3 x 3    =   2 x 32

Q3.        48 = 2 x 2 x 2 x 2 x 3    =  24 x 3

Q4.      We use the division method as shown below:

               

                  56 = 2 x 2 x 2 x 7     =  23 x 7

Q5.        [Hints: 2 x 45 = 90, 3 x 15 = 45, 3 x 5 = 15, 5 x 1 = 5]

                   90 = 2 x 3 x 3 x 5 =  2 x 32 x 5

Q6.        [Hints:  2 x 68 = 136, 2 x 34 = 68, 2 x 17 = 34, 17 x 1 = 17]

                   136 = 2 x 2 x 2 x 17  = 23 x 17

Q7.      [Hints: 2 x 126 = 252, 2 x 63 = 126, 3 x 21 = 63, 3 x 7 = 21, 7 x 1 = 7]

               252 = 2 x 2 x 3 x 3 x 7 x 1 = 22 x 32 x 7

Q8.         We use the division method as shown below:

               

                  420 = 2 x 2 x 3 x 7 x 5   =  22 x 3 x 5 x 7

Q9.      637  We use the division method as shown below:

 [Hints: 7 x 91 = 637, 7 x 13 = 91, 13 x 1 = 13 ]

           

              637 = 7 x 7 x 13  = 72 x 13    www. rsmaths99.com

Q10.    945   [ Hints: 3 x 315 = 945, 3 x 105 = 315, 3 x 35 = 105, 5 x 7 = 35, 7 x 1 = 7 ]

                  3 x 3 x 3 x 5 x 7 x 1  = 33 x 5 x 7

Q11.    1224    [Hints: 2 x 612 = 1224,2 x 306 = 612, 2 x 153 = 306,

3 x 51 = 153, 3 x 17 = 51, 17 x 1 = 17]

              1224 = 2 x 2 x2 x 3 x 3 x 17    = 23 x 32 x 17

Q12.    1323  [Hints: 3 x 441, 3 x 147= 441, 3 x 49 = 147, 7 x 7 = 49, 7 x 1 = 7]

               1323 = 3 x 3 x 3 x 7 x 7 x 1  = 33 x 72

Q13.    8712  [Hints: 2 x 4356 = 8712, 2 x 2178 = 4356, 2 x 1089 = 2178,

3 x 363 = 1089, 3 x 121]

              2 x 2 x 2 x 3 x 3 x 11 x 11  = 23 x 32 x 112

Q14.    9371    We use the division method as shown below:

           

                  9371 = 7 x 11 x 11 x 11 x 1     = 7 x 113

Q15.   1035    We use the division method as shown below:

              

                  1035  = 3 x 3 x 5 x 23  = 32 x 5 x 23

Q16.   1197  We use the division method as shown below:

               

                   1197  = 3 x 3 x 7 x 19  = 32 x 7 x 19

Q17.     4641   We use the division method as shown below:

               

                  4641 = 3 x 7 x 13 x 17

Q18.     4335   We use the division method as shown below:

               

              4335 = 3 x 5 x 17 x 17  = 3 x 5 x 172

Q19.   2907  We use the division method as shown below:

                   

                  3 x 3 x 17 x 19    = 32 x 17 x 19       www. rsmaths99.com

Q20.   13915  We use the division method as shown below:

               

                   13915 = 5 x 11 x 11 x 23  = 3 x 112 x 23    

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Exercise -2D

Q1.      84, 98

           

                84 = 2 x 2 x 3 x 7   = 22 x 3 x 7

            98 = 2 x 7 x 7     =  2 x 72

              HCF of the given number = 2 x 7 = 14

Q2.       170, 238

            170 [Hints: 2 x 85 = 170, 5 x 17 = 85, 17 x 1= 17]

            238 [Hints: 2 x 119 = 238, 7 x 17 = 119, 17 x 1 = 17]

            170 = 2 x 5 x 17

            238 = 2 x 5 x 17

              HCF of the given number = 2 x 17 = 34

 Q3.      504, 980

            504 [Hints: 2 x 252 = 504, 2 x 126, 2 x 63= 126, 3 x 21=63, 3 x 7 = 21, 7 x 1 = 7]

            980 [Hints: 2 x 490 = 980, 2 x 245 = 490, 5 x 49 = 245, 7 x 7 = 49, 7 x 1 = 7]

            504 = 2 x 2 x 2 x 3 x 3 x 7 = 23 x 32 x 7

            980 = 2 x 2 x 5 x 7 x 7   = 22 x 5 x 72

              HCF of the given number = 22 x 7 = 28

Q4.     

Find the HCF, using the division method:

Now, 72 = 2 x 2 x 2 x 3 x 3  = 23 x 32

            108 = 2 x 2 x 3 x 3 x 3 = 22 x 33

            180 = 2 x 2 x 3 x 3 x 5  = 22 x 32 x 5

              HCF = 22 x 32 = 36

 

Q10.   58, 70               www. rsmaths99.com

           

              HCF of 58 and 70 is 2.

Q6.      Given nos. are 106, 159 and 571

           

           

            Now, 106 = 2 x 53

            159 = 3 x 53

            371 = 7 x 53

              HCF = 53

Q7.      Given nos. are 272 & 425

           

            Now, 272 = 2 x 2 x 2 x 2 x 17

                        425 = 5 x 5 x 17

              HCF  is 17.

Q8.      Given nos. are 144, 252 and 630

           

            Now, 144 = 2 x 2 x 2 x 2 x 3 x 3

                        252 = 2 x 2 x 3 x 3 x 7

                        630 = 2x 3 x 3 x 5 x 7

                          HCF  is 2 x 3 x 3 = 18

Q9.     

           

                     

                       

 

 

 

 

 

 

 

EXERCISE – 2E

 

 

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