Question

If HCF of 66 and 99 is expressible in the form of \(55m - 132\), then the value of m is :

• A. 4
• B. 2
• C. 1
• D. 3

Hint:

Double check your division: \(55 \times 3 = 165\).
Linear equations like this are highly scoring, so write out every step clearly.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given two numbers, 66 and 99. Their Highest Common Factor (HCF) is represented as \(55m - 132\). We need to determine the value of \(m\).

Step 2: Key Formula or Approach:
- First, calculate the actual HCF of 66 and 99 using prime factorization or Euclid's division algorithm.
- Equate the calculated HCF to \(55m - 132\) and solve for \(m\).

Step 3: Detailed Explanation:

• Find prime factorizations:
\[ 66 = 2 \times 3 \times 11 \]
\[ 99 = 3^2 \times 11 \]

• Determine the HCF by taking the lowest power of common prime factors:
\[ \text{HCF} = 3^1 \times 11^1 = 33 \]

• Equate the HCF to the given expression:
\[ 55m - 132 = 33 \]

• Solve the equation:
\[ 55m = 33 + 132 \]
\[ 55m = 165 \]
\[ m = \frac{165}{55} = 3 \]


Step 4: Final Answer:
The value of \(m\) is 3.