Question

Use Euclid's algorithm to find the HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.​

Answer 1

Solution:

Here we have to find HCF of 1190 and 1445 and express the HCF in the form 1190m + 1445n.

1445 = 1190 × 1 + 255

1190 = 255 × 4 + 170

255 = 170 × 1 + 85

170 = 85 × 2 + 0

So, now the remainder is 0, then HCF is 85

Now,

85 = 255 - 170

= (1445 - 1190) - (1190 - 255 × 4)

= 1445 - 1190 - 1190 + 255 × 4

= 1445 - 1190 × 2 + (1445 - 1190) × 4

= 1445 - 1190 × 2 + 1445 × 4 - 1190 × 4

= 1445 × 5 - 1190 × 6

= 1190 × (- 6) + 1445 × 5

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

Answer 2

Answer:

Here we have to find HCF of 1190 and 1445 and express the HCF in the form 1190m + 1445n.

1445 = 1190 × 1 + 255

1190 = 255 × 4 + 170

255 = 170 × 1 + 85

170 = 85 × 2 + 0

So, now the remainder is 0, then HCF is 85

Now,

85 = 255 - 170

= (1445 - 1190) - (1190 - 255 × 4)

= 1445 - 1190 - 1190 + 255 × 4

= 1445 - 1190 × 2 + (1445 - 1190) × 4

= 1445 - 1190 × 2 + 1445 × 4 - 1190 × 4

= 1445 × 5 - 1190 × 6

= 1190 × (- 6) + 1445 × 5

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