Question

Express in the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways. Please show in process ​

Answer 1

Answer:

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Step-by-step explanation:

Using Euclid's Division Algorithm,

468 = (222 × 2) + 24

222 = (24 × 9) + 6

24 = (6 × 4) + 0

Since the remainder is 0, the HCF = 6

Using the above equations, we get

6 = 222 - (24 × 9)

6 = 222 - {(468 – 222 × 2) × 9 [where 468 = 222 × 2 + 24]

6 = 222 - {468 × 9 – 222 × 2 × 9}

6 = 222 - (468 × 9) + (222 × 18)

6 = 222 +(222 × 18) - (468 × 9)

6 = 222[1 + 18] – 468 x 9

6 = 222 × 19 – 468 × 9

6 = 468 × (-9) + 222 × 19

Hence, HCF of 468 and 222 in the form of 468x + 222y is 468 × (-9) + 222 × 19.

Answered by Rebecca Fernandes | 27th Nov, 2017, 12:49: PM

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second method

To show: HCF of 468 and 222 as 468x + 222y in two different ways. Now, we need to express the HCF of 468 and 222 as 468x + 222y where x and y are any two integers. Therefore, the HCF of 468 and 222 is written in the form of 468x + 222y where, -9 and 19 are the two integers.

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