Question

if d is the HCF of 30and72 find the values of x and y satisfying d=30x+72y also show that x and y are not unique

Answer 1

Hi friend,

Euclid division lemma:-

a = bq + r

0 ≤ r < b

a > b

72 = 30 × 2 + 12

30 = 12 × 2 + 6

12 = 6 × 2 + 0

As the remainder is 0,we can not proceed further.

HCF (30,72) = 6

d = 6

6 = 30 - 12×2

=30 - {72-30(2)}×2

= 30 - 72×2+30×4

= 30×5 - 72×2

= 30×5 + 72×(-2)

= 30x + 72 y

x = 5 and y = -2

Therefore, x and y are not unique.

Hope it helps

Answer 2

Factors of 30=2×3×5
Factors of 72=2×2×2×3×3

Highest Common factor=2×3=6=d

i→x=1/5,y=0
ii→x=0,y=1/12
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And so on❕❕❕❕