Question

Express the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways.

Answer 1

In order to take out H.C.F we will use following steps,

468 = 222 × 2 + 24 ___(1)

222 = 24 × 9 + 6 ___(2)

24 = 6 × 4 + 0

Hence H.C.F of 468 and 222 is 6.

Using 2nd equation we get,

222 = 24 × 9 + 6

222 - 24 × 9 = 6 ___(3)

Using 1st equation we get,

468 - 222 × 2 = 24 ___(4)

On susbtituting eq(4) in (3) we get,

222 - (468 - 222 × 2) × 9 = 6

222 - 468 + 222 × 18 = 6

468(-1) + 2 × 222 × 18 = 6

468(-1) + 222(36) = 6

468x + 222y = 6 where, x = - 1 and y = 36.

[Note : x and y aren't unique which means that they can have other values that these two also ]

Answer 2

Comparing the solved eq with the given we will get

X=-9

y=19