Question

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

Answer 1

==> 468 = 222 × 2 + 24

==> 222 = 24 × 9 + 6

==> 24 = 6 × 4 + 0

HCF = 6

==> 6 = 222 - ( 24 × 9)

==> 6 = 222 - ( (468 - 222 × 2 ) × 9 )

==> 6 = 222 - ( 468 × 9 - 222 × 9 × 2 )

==> 6 = 222 - 468 × 9 + 222 × 18

==> 6 = 222 ( 1 + 18 ) + 468 × -9

==> 6 = 222 × 19 + 468 × -9

==> 6 = 468 × -9 + 222 × 19

Here,

6 = 468x + 222y

where,

==> x = -9

==> y = 19