Question

find the HCF of 56 and 24 and express it in the linear combination of 56x + 24y​

Answer 1

therefore x = -68 and y = 53

HENCE , x and y are not unique

Step-by-step explanation:

BY APPLYING EUCLID's DIVISION LEMMA TO 56 AND 72 :

72 = 56 × 1 +16 ------------ (1)

56 = 16 × 3 + 8 ------------ (2)

16 = 8 × 2 + 0 -------------- (3)

THEREFORE HCF OF 56 AND 72 = 8

FROM (2) -- 8 = 56 - 16 ×3

8 = 56 - (72-56×1) ×3 (from 1)

8 = 56 - 3 × 72 + 56 × 3

8 = 56 × 4 + (-3) × 72

therefore , x = 4 and y = -3

Now, 8 = 56 × 4 + (-3) × 72

8 = 56 × 4 + (-3) × 72 - 56 × 72 + 56 × 72

8 = 56 × 4 -56 × 72 + (-3) × 72 + 56 ×72

8 = 56 × (4-72) + {(-3) + 56} × 72

8 = 56 × (-68) + (53) × 72

therefore x = -68 and y = 53

HENCE , x and y are not unique

Answer 2

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