Question

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

Answer 1

By Euclid’s division algorithm,

HCF of 468 and 222 is
468 = (222 x 2) + 24  ----------------------(1)
222 = (24 x 9) + 6   ------------------------(2)
24 = (6 x 4) + 0  

So the HCF of 468 and 222 is 6.
Now we have to write 6 as 468x + 222y

6 = 222 - (24 x 9)  --------------- [ from (2) ]

Now write 24 as (468 – 222 x 2) -------------- [ from (1) ]
⇒ 6 = 222 - {(468 – 222 x 2) x 9               
       = 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

So HCF of 468 and 222 is (468 x -9 + 222 x 19) in the form 468x + 222y

Answer 2

here is the answer to your question