Question

if the hcf of 468 and 222 is d. find x and y such that 468x+222y=d

Answer 1

HCF of 468 and 222

468 = (222 x 2) + 24
222 = (24 x 9) + 6
24 = (6 x 4) + 0
 
Therefore, HCF = 6

6 = 222 - (24 x 9)
   = 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.