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

To find the Highest Common Factor (HCF) of 960 and 432, we can use the prime factorization method. Let's break down both numbers into their prime factors and then determine the common factors.

Step 1: Prime Factorization of 960

• Divide 960 by 2: \(960 \div 2 = 480\)
• Divide 480 by 2: \(480 \div 2 = 240\)
• Divide 240 by 2: \(240 \div 2 = 120\)
• Divide 120 by 2: \(120 \div 2 = 60\)
• Divide 60 by 2: \(60 \div 2 = 30\)
• Divide 30 by 2: \(30 \div 2 = 15\)
• 15 is divisible by 3: \(15 \div 3 = 5\)
• 5 is a prime number.

So, the prime factorization of 960 is: \(2^6 \times 3 \times 5\)

Step 2: Prime Factorization of 432

• Divide 432 by 2: \(432 \div 2 = 216\)
• Divide 216 by 2: \(216 \div 2 = 108\)
• Divide 108 by 2: \(108 \div 2 = 54\)
• Divide 54 by 2: \(54 \div 2 = 27\)
• 27 is divisible by 3: \(27 \div 3 = 9\)
• 9 is divisible by 3: \(9 \div 3 = 3\)
• 3 is a prime number.

So, the prime factorization of 432 is: \(2^4 \times 3^3\)

Step 3: Finding the HCF

To find the HCF, identify the lowest power of all common prime factors from both numbers.

• The common prime factors are 2 and 3.
• Lowest power of 2: \(2^4\)
• Lowest power of 3: \(3^1\)

Therefore, the HCF is: \(2^4 \times 3 = 16 \times 3 = 48\)

Thus, the HCF of 960 and 432 is 48.