When the HCF of 468 and 222 is written in the form of 468 x + 222 y then the value of x and y is

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Linear Equations in One Variable

Question

When the HCF of

468

and

222

is written in the form of

468 x + 222 y

then the value of

x

and

y

x = - 9 a n d y = 19

x = 9 a n d y = - 19

x = 9 a n d y = 19

x = - 9 a n d y = - 19

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

According to the definition of Euclid's theorem,

a = b \times q + r

where

0 \leq r &lt; b .

HCF of

468

and

222

468 = (222 \times 2) + 24

222 = (24 \times 9) + 6

24 = (6 \times 4) + 0

∴ H C F = 6

6 = 222 - (24 \times 9)

= 222 - [(468 - 222 \times 2) \times 9],

[where

468 = 222 \times 2 + 24

]

= 222 - [468 \times 9 - 222 \times 2 \times 9]

= 222 - (468 \times 9) - (222 \times 18)

= 222 + (222 \times 18) - (468 \times 9)

= 222 [1 + 18] -, 468 \times 9

= 222 \times 19 -, 468 \times 9

, = 468 \times - 9 + 222 \times 19

∴ x = - 9

and

y = 19