Question

HCF \((132, 77)\) is:

• A. \(11\)
• B. \(77\)
• C. \(22\)
• D. \(44\)

Answer 1

The Correct Option is A

Problem:
We are asked to find the Highest Common Factor (HCF) of the numbers 132 and 77.

Step 1: Understand what HCF means
The HCF (also called GCD – Greatest Common Divisor) of two numbers is the largest number that divides both of them exactly, without leaving a remainder.

Step 2: Prime factorization of both numbers
Let’s find the prime factors of 132:
132 = 2 × 2 × 3 × 11 = \(2^2 \times 3 \times 11\)

Now the prime factors of 77:
77 = 7 × 11 = \(7 \times 11\)

Step 3: Identify common factors
- 132 has: \(2^2, 3, 11\)
- 77 has: \(7, 11\)
So, the common factor is 11

Final Answer:
The HCF of 132 and 77 is 11.