If HCF of 210 and 55 is expressed in the form of 210 × 5 - 55y, find the value of y².

• A) 381
• B) 368
• C) 361
• D) 19

To find the HCF (Highest Common Factor) of 210 and 55, we can use the Euclidean algorithm. First, we divide 210 by 55:

Step 1: Perform Division

210 divided by 55 gives a quotient of 3 and a remainder of 45:

• 210 = 55 × 3 + 45

Step 2: Continue with the Remainder

Next, we take 55 and divide it by the remainder 45:

• 55 = 45 × 1 + 10

Step 3: Repeat the Process

Now, we divide 45 by 10:

• 45 = 10 × 4 + 5

Step 4: Final Division

Next, we divide 10 by 5:

• 10 = 5 × 2 + 0

Identify the HCF

Since the remainder is now 0, the last non-zero remainder is the HCF. Thus, the HCF of 210 and 55 is 5.

Expressing HCF in the Given Form

We need to express 5 in the form of:

5 = 210 × 5 - 55y

Setting Up the Equation

Rearranging gives:

55y = 210 × 5 - 5

55y = 1050 - 5

55y = 1045

Solving for y

Now, divide both sides by 55:

y = 1045 / 55

y = 19

Finding y²

Now, we calculate:

y² = 19² = 361

Final Answer

The value of y² is 361. Therefore, the correct option is C) 361.