Question

If The Hcf Of 152 And 272 Is Expressed In The Form Of 272X+152Y Find X And Y

Answer 1

Finding the HCF of 152 and 272.

By using Euclids Division Lemma,

a = bq + r

a = 272, b = 152

[Check Attachment for the Division]

272 = 152 × 1 + 120 → ..eq1

152 = 120 × 1 + 32 → ..eq2

120 = 32 × 3 +24 → ..eq3

32 = 24 × 1 + 8 → ..eq4

24 = $\boxed {\sf 8}$ × 3 + 0

$\large\boxed{\sf{H.C.F = 8}}$

Finding 'x' and 'y'.

8 = 32 - 24 × 1 [From Eq4]

8 = 32 - [120 - 32 × 3] × 1 [From Eq3]

8 = 32 - 120 + 32(-3)

8 = -120 + 32(-4)

8 = -120 + [152 - 120 × 1] (-4) [From Eq2]

8 = -120 + 152(-4) + 120(4)

8 = 120(-5) + 152(-4)

8 = [272 - 152 ×1](-5) + 152(-4) [From Eq1]

8 = 272(-5) - 152(-5) + 152(-4)

8 = 272(-5) + 152(9)

8 = 272x + 152y

∴ x = -5

∴ y = 9

Crosschecking the Answer:

8 = 272x + 152y

8 = 272(-5) + 152(9)

8 = -1360 + 1368

8 = 8

LHS = RHS

Hence the Answer is correct.