Express the hcf of 234 and 111 as 234x+111y, where x and y are integer

1.	Express the hcf of 234 and 111 as 234x+111y, where x and y are integers
Answer» HCF of 234 and 111234 = 2 x 3 x 3 x 13111 = 3 x 37Therefore, HCF = 3So we can write it3 = 111 - (12 x 9)3 = 111 - {(234 – 111 x 2) x 9}[where 12 = 234 - 111 x 2]3 = 111 - {234 x 9 – 222 x 2 x 9}3 = 111 - (234 x 9) + (111 x 18)3 = 111 + (111 x 18) - (234 x 9)3 = 111[1 + 18] – 234 x 93 = 111 x 19 – 234 x 93 = 234 x (-9) + 222 x 19Hence, HCF of 234 and 111 in the form of234x + 111y is 234 x (-9) + 111 x 19\xa0

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