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: Find the HCF using Euclid's division algorithm instead of prime factorisation.
\[ 99 = 66 \times 1 + 33 \]
\[ 66 = 33 \times 2 + 0 \]
Since the remainder is now 0, the HCF is the last non-zero remainder.
Step 2: Identify the HCF.
\[ \text{HCF}(66, 99) = 33 \]
Step 3: Solve for m.
\[ 55m - 132 = 33 \implies 55m = 165 \implies m = 3 \]
\[ \boxed{m = 3} \]