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

Asked by Prachi | 22nd Apr, 2017, 09:22: PM

Expert Answer:

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