ILLUSTRATION : 2 Let us find the H.C.F. of 60 and 108 using the Euclid's Division Algorithm.

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SOLUTION: : Step (i): since, ( 108>60 ) applying Euclid's Lemma to 60 and 108 , we have [ 108=60 times 1+48 text { where } 0 leq 48<60 ] Step (ii): Since, remainder ( 48 eq 0 ) So, again applying the division lemma to 60 and ( 48, ) we have [ 60=48 times 1+12 text { where } 0 leq 12<48 ] Step (iii) : Again remainder ( 12 eq 0 ) so applying division lemma to 48 and ( 12, ) we get ( 48=12 times 4+0, ) Here remainder is zero. Therefore, 12 is the required ( mathrm{H.C.F.} )

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