Question

use euclids division lemma to find hcf of 1190 and 1445. Express the HCF in the form of 1190m+1445n.

Answer 1

Answer to the question:
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+2551190=255x4+170255=170x1+85170=85x2+0
We have found r=0Hence, 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) .