Question

The HCF of 468 and 222 can be expressed as 468x + 222y, where x and y are integers. Find the value of x + y.

• A. 8
• B. 10
• C. -26
• D. -8

Answer 1

The correct option is B 10

The HCF of 468 and 222 using Euclid’s division algorithm:

468 = 222 × 2 + 24 … (1)
⇒ 222 = 24 × 9 + 6 … (2)
⇒ 24 = 6 × 4

Hence, the HCF of 468 and 222 is 6.

From (2), 6 = 222 - 24 × 9 … (3)
From (1), 24 = 468 - 222 × 2 … (4)

Substituting the value of 24 from (4) into (3),
6 = 222 - [(468 - 222 × 2) × 9]
⇒ 6 = 222 - 468 × 9 + 222 × 18
⇒ 6 = 468 × (-9) + 222 × (19)

Thus, x = -9, y = 19
⇒ x + y = -9 + 19 = 10