Express the HCF of 468 and 222 as 468x + 222y where x and y are intege

1.	Express the HCF of 468 and 222 as 468x + 222y where x and y are integers.
Answer» By Euclid’s division algorithm,HCF of 468 and 222 is468 = (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 + 222y6 = 222 - (24 x 9) ---------------\xa0[ from (2) ]Now write 24 as (468 – 222 x 2)\xa0--------------\xa0[ from (1) ]⇒ 6\xa0= 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 19So HCF of 468 and 222 is (468 x -9 + 222 x 19) in the form 468x + 222y.

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