Question

use euclid's division lemma to find HCF of 1190 and 1445. Express the HCF in the form of 1190+1445n

Answer 1

Here is an answer :
1445=1190 x 1 + 255

1190=255 x 4 +170

255=170 x 1 + 85

170=85 x 2 + 0

HCF = 85 

Now,                                     

 85 = 255 - 170

      =(1445-1190)-(1190-255 x 4)

      =1445-1190-1190+255 x 4

      =1445-1190 x 2+(1445-1190) x 4

      =1445-1190 x 2+1445 x 4-1190 x 4

      =1445 x 5 - 1190 x 6

      =1190 x (-6) + 1445 x 5

      =1190m + 1445n, where m= -6 and n = 5