Question

The HCF of 960 and 432 is :

• A. 48
• B. 54
• C. 72
• D. 36

Hint:

To check your answer, divide both numbers by the HCF. \( 960/48 = 20 \) and \( 432/48 = 9 \). Since 20 and 9 have no common factors other than 1, 48 is indeed the HCF.

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 this using Prime Factorization or Euclid's Division Algorithm.
Step 2: Key Formula or Approach:
Euclid's Division Lemma: \( a = bq + r \), where \( 0 \leq r<b \). Repeat the process until \( r = 0 \); the last divisor is the HCF.
Step 3: Detailed Explanation:
1. Apply Euclid's Division Algorithm on 960 and 432: \[ 960 = 432 \times 2 + 96 \] 2. Now take 432 as the dividend and 96 as the divisor: \[ 432 = 96 \times 4 + 48 \] 3. Now take 96 as the dividend and 48 as the divisor: \[ 96 = 48 \times 2 + 0 \] 4. Since the remainder is now 0, the divisor at this stage is the HCF.
Step 4: Final Answer:
The HCF of 960 and 432 is 48.