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# USE EUCLID'S DIVISION ALGORITHM TO FIND THE H.C.F OF 1190 AND1445 AND EXPRESS THE HCF IN THE FORM OF 1190m+1445n

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Solution

## We know that Euclid's division Lemma is x and y for any two positive integers, there exist unique integers q and r satisfactorily x = yq + r, where 0 ≤ r <y. In case r=0 then y will be the HCF. 1445=1190x1+255 1190=255x4+170 255=170x1+85 170=85x2+0 We have found r=0 Hence, HCF(1190,1445)=85 So, now 85 = 255 - 170 =(1445-1190)-(1190-1020) =(1445-1190)-(1190-255x4) =1445-1190-1190+255x4 =1445-2×1190+(1445-1190)x4 =1445-2×1190+1445x4-1190x4 =1445+1445×4-2×1190-1190×4 =1445x5-1190x6 =-1190×6+1445×5 =1190x(-6)+1445x5 =1190m+1445n (where m=-6 and n=5)

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