Express the HCF of 468 and 222 as 468x + 222y where x,y are integersin two different waxs.

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

1.	Express the HCF of 468 and 222 as 468x + 222y where x,y are integersin two different waxs.
Answer» Given integers are 468 and 222 where 468 > 222.By applying Euclid’s division lemma, we get 468 = 222 × 2 + 24 …(i)Since remainder ≠ 0, apply division lemma on division 222 and remainder 24 222 = 24 × 9 + 6 …(ii)Since remainder ≠ 0, apply division lemma on division 24 and remainder 6 24 = 6 × 4 + 0 …(iii)We observe that the remainder = 0, so the last divisor 6 is the HCF of the 468 and 222From (ii) we have6 = 222 – 24 × 9⇒ 6 = 222 – [468 – 222 × 2] × 9 [Substituting 24 = 468 – 222 × 2 from (i)]⇒ 6 = 222 – 468 × 9 – 222 × 18⇒ 6 = 222y + 468x, where x = −9 and y = 19⇒ 6 = 222 × 19 – 468 × 9