ACTIVITY 01

CLASS X

OBJECTIVE

TO FIND THE HCF OF TWONUMBERS EXPERIMENTALLYBASED ON EUCLID’SDIVISION LEMMA

MATERIALS REQUIRED

CARD BOARD SHEETSGLAZED PAPERS OF DIFFERENT COLOURSSCISSORSRULERSKETCH PEN GLUE ETC.,

METHOD OF CONSTRUCTIONCUT OUT ONE STRIP OF LENGTH a UNITS, ONESTRIP OF LENGTH b UNITS [ b<a], TWO STRIPS EACH OF LENGTH c UNITS [ c<b], ONE STRIP OF LENGTH d UNITS [ d<c] AND TWO STRIPS EACH OF LENGTH e UNITS [ e<d] FROM THE CARDBOARD.

METHOD OF CONSTRUCTION

COVER THESE STRIPS IN DIFFERENT COLOURS USING GLAZED PAPERS AS SHOWN INFIG 1 AND FIG 2.

ab

FIGURES 3,4 & 5

C C

d

e e

Fig 6, 7, 8 and 9STICK THESE STRIPS ON THE OTHER CARDBOARD SHEET AS SHOWN IN THE FIG.6 TO FIG.9

c FIG.6

ab

c

d FIG 7.

FIG . 8 FIG. 9

bc

c

c d

d e e

FIG CONTINUED…

d

e

DEMONSTRATION

AS PER EUCLID’S DIVISION LEMMA, [ a= bq + r]

FIG. 6 DEPICTS a = b X 1 + c Here, q = 1, r = c

ab

c

FIG.7 DEPICTS b = c X 2 + d

Here, q = 2 , r= d

bc

c

d

FIG.8 DEPICTS C = d X 1 + eHere, q = 1 , r= e

FIG.8 DEPICTS d = e X 2 + 0Here, q = 2 , r= 0

c d e

d e e

As per assumption in Euclid Division Algorithm,HCF of a and b = HCF of b and c = HCF of c and d = HCF of d and eThe HCF of d and e is equal to e.So, HCF of a and b = e.

OBSERVATIONOn actual measurement [ in mm ]a = _____________, b = ________________

c = ______________, d = _________________

e = _______________

So, HCF of _________ and ________ = ________

CONCLUSION

The process depicted can be used forFinding The HCF of two or morenumbers, which is Known as finding HCF of numbers by Division Method.

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