Question

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

Answer 1

after dividing 468 by 222 the hcf is given by
HCF of 468 and 222

468 = (222 x 2) + 24.......(1)
222 = (24 x 9) + 6..........(2)
24 = (6 x 4) + 0........(3)
 
Therefore, HCF = 6
from equation 2 we have
6=222-(24x9)

=222 - {(468 – 222 x 2) x 9 [where 468 = 222
x-2+24]

= 222 - {468 x 9 – 222 x 2 x 9}
   = 222 - (468 x 9) + (222 x 18)
   = 222 + (222 x 18) - (468 x 9)
   = 222[1 + 18] – 468 x 9
   = 222 x 19 – 468 x 9
   = 468 x -9 + 222 x 19

Hence, HCF of 468 and 222 in the form of 468x + 222y is 468 x -9 + 222 x 19




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