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Express the hcf of 234 and …

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

Posted by Himanshi Gupta 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 7 months ago

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

Hence, HCF of 234 and 111 in the form of
234x + 111y is 234 x (-9) + 111 x 19

1Thank You

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