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

The problem requires us to find the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of the numbers 960 and 432. Let's solve this step-by-step using the Prime Factorization method:

1. Prime factorize each number:
   • 960:
     • 960 is even, so divide by 2: \(960 \div 2 = 480\)
     • 480 is even, continue dividing by 2: \(480 \div 2 = 240\)
     • Continue dividing: \(240 \div 2 = 120\)
     • And again: \(120 \div 2 = 60\)
     • 60 is even, divide: \(60 \div 2 = 30\)
     • Finally: \(30 \div 2 = 15\)
     • 15 is not even, divide by 3: \(15 \div 3 = 5\)
     • 5 is a prime number.
   • The prime factorization of 960 is: \(2^6 \times 3 \times 5\)
   • 432:
     • 432 is even, divide by 2: \(432 \div 2 = 216\)
     • Continue with 2: \(216 \div 2 = 108\)
     • And again: \(108 \div 2 = 54\)
     • 54 is even: \(54 \div 2 = 27\)
     • 27 is divisible by 3: \(27 \div 3 = 9\)
     • And again: \(9 \div 3 = 3\)
     • 3 is a prime number.
   • The prime factorization of 432 is: \(2^4 \times 3^3\)
2. Identify the common factors with the smallest power in each term:
   • For the prime number 2, the minimum power is \(2^4\).
   • For the prime number 3, the minimum power is \(3^1\).
3. Multiply these common prime factors to find the HCF:
   • \(HCF = 2^4 \times 3 = 16 \times 3 = 48\)

Thus, the HCF of 960 and 432 is 48. Therefore, the correct answer is Option 1: 48.