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

Express the HCF of 468 and 222 as 468x + 222y where x,y are integers i

1.	Express the HCF of 468 and 222 as 468x + 222y where x,y are integers in two different ways
Answer» HCF of 468 and 222468 = (222 x 2) + 24222 = (24 x 9) + 624 = (6 x 4) + 0\xa0Therefore, HCF = 66 = 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 19Hence, HCF of 468 and 222 in the form of 468x + 222y is 468 x -9 + 222 x 19.