Question

The HCF of 960 and 432 is :

• A. 48
• B. 54
• C. 72
• D. 36

Hint:

In multiple-choice questions, you can quickly check which option divides both numbers.
Try the largest option first if looking for HCF. 72 doesn't divide 960 exactly (\(960/72 \approx 13.3\)). 48 divides 960 (\(48 \times 20\)) and 432 (\(48 \times 9\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Highest Common Factor (HCF) is the largest positive integer that divides each of the integers without leaving a remainder. We can find it using Euclid's Division Algorithm or Prime Factorization.
Step 2: Key Formula or Approach:
We will use Euclid's Division Algorithm: \(a = bq + r\).
Step 3: Detailed Explanation:
Step 1: Since \(960>432\), apply Euclid's division lemma:
\[ 960 = 432 \times 2 + 96 \]
Step 2: Since the remainder \(96 \neq 0\), apply the lemma to 432 and 96:
\[ 432 = 96 \times 4 + 48 \]
Step 3: Since the remainder \(48 \neq 0\), apply the lemma to 96 and 48:
\[ 96 = 48 \times 2 + 0 \]
The remainder has now become zero. The divisor at this stage is 48.
Step 4: Final Answer:
Therefore, the HCF of 960 and 432 is 48.