Express the HCF of 468 and 222 as 468+22y where x and y are integers in twice different ways

Express the HCF of 468 and 222 as 468+22y where x and y are integers i

1.	Express the HCF of 468 and 222 as 468+22y where x and y are integers in twice different ways
Answer» Given integers are 468 and 222, where 468 > 222By applying Euclid’s division lemma, we get468 = 222 {tex}\\times{/tex}\xa02 + 24.222 = 24 {tex}\\times{/tex}\xa09 + 6.24 = 6 {tex}\\times{/tex}\xa04 + 0.We observe that remainder is 0. So the last divisor 6 is the H.C.F. of 468 and 222 .6 = 222 - 24 {tex}\\times{/tex}\xa096 = 222 - (468 - 222 {tex}\\times{/tex}\xa02) {tex}\\times{/tex}\xa09 [Substituting 24 = 468 - 222 {tex}\\times{/tex}\xa02]6 = 222 - 468 × 9 + 222 {tex}\\times{/tex}\xa0186 = 222(1 + 18) - 468 × 96 = 222 {tex}\\times{/tex}\xa019 - 468 {tex}\\times{/tex}\xa096 = 468 ×\xa0(-9) + 222 ×\xa0196 = 468x +\xa0222y where x = - 9 and y = 19.Hence, obtained.