Question

If the HCF of 152 and 272 is expressible in the form 272x + 152y where x and y are integers, then find x and y.

Answer 1

x = -5 & y = 9 if  the HCF of 152 and 272 is expressed in the form 272x + 152y . x , y being integer

Finding the HCF of 152 and 272.

a = bq + r

a = 272, b = 152

272 = 152 × 1 + 120

152 = 120 × 1 + 32

120 = 32 × 3 +24

32 = 24 × 1 + 8

24 = 8 * 3

HCF = 8

Finding 'x' and 'y'.

8 = 32 - 24 × 1

8 = 32 - [120 - 32 × 3]

8 = 32 - 120 + 32(3)

8 = -120 + 32(4)

8 = -120 + [152 - 120 × 1] (4)

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

8 =  152(4) - 120(5)

8 = 152(4) - (272 - 152*1)5

8 = 152(4)  -272(5) + 152(5)

8 =  152(9)  -272(5)

8 = 272(-5) +  152(9)

Comparing with

8 = 272x + 152y

x = -5

y = 9

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