Question

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

Answer 1

HCF of 468 and 222

468 = (222 x 2) + 24
222 = (24 x 9) + 6
24 = (6 x 4) + 0

Therefore, HCF = 6

6 = 222 - (24 × 9)

6 = 222 - {(468 – 222 × 2) × 9}

6 = 222 - {468 × 9 – 222 × 18}

6 = 222 + (222 × 18) - (468 × 9)

6 = 222(1 + 18) – 468 × 9

6 = 222 × 19 – 468 × 9

6 = 468 × (-9) + 222 × 19

Now compare this equation with "D = 468 X + 222 Y", therefore X = -9 and Y = 19