Question

if the hcf of 420 and 110 is expressible in the from of 420×5+110x findx

Answer 1

Euclid's division lemma:-

a=bq+r

0 ≤ r ≤ b

420 = 110 × 3 + 90

110 = 90 × 1 + 20

90 = 20 × 4 + 10

20 = 10 × 2 + 0

HCF of 420 and 110 is 20.

20 is expressed in the form 420×5+110x

20 = 420(5) + 110x

20 = 2100 + 110x

110x = 20-2100

110x = -2080

x = -2080/110

x = -18.90 (approx.)

Hope it helps

Answer 2

a=bq+r

0 ≤ r ≤ b

420 = 110 × 3 + 90

110 = 90 × 1 + 20

90 = 20 × 4 + 10

20 = 10 × 2 + 0

HCF of 420 and 110 is 20.

20 is expressed in the form 420×5+110x

20 = 420(5) + 110x

20 = 2100 + 110x

110x = 20-2100

110x = -2080

x = -2080/110