If D is the HCF of 468 and 222, find the value of integers X and Y, which satisfies that D = 468 X + 222 Y.

The largest possible number which divides the given numbers exactly without any remainder is called the HCF (Highest Common Factor).

Answer: HCF of 468 and 222 is 6, the values of X and Y are X = -9 and Y = 19

HCF of 468 and 222 is the highest number that divides 468 and 222 exactly leaving the remainder 0.

Explanation:

Here we are using Euclid's Division Algorithm to find the HCF of 468 and 222.

468 = (222 × 2) + 24

222 = (24 × 9) + 6

24 = (6 × 4) + 0

Therefore, the HCF of 468 and 222 is, 6.

So, D = 6

Now to calculate the values of X and Y we need to work as:

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

Therefore, the HCF of 468 and 222 is 6, the values of X and Y are; X = -9 and Y = 19