Question

Express the HCF of 234 and 111 as 234x + 111y , where x and y are integers.

Answer 1

Answer:

HCF of 234 and 111

234 = 2 x 3 x 3 x 13

111 = 3 x 37

Therefore, HCF = 3

So we can write it

3 = 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 9

3 = 111 x 19 – 234 x 9

3 = 234 x (-9) + 222 x 19

Answer 2

Answer:

refer the above photo

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