The HCF of 64, 28 and 96 is :

Options

A. 2
B. 4
C. 1
D. 8

Answer

To find the HCF (Highest Common Factor) of the numbers 64, 28, and 96, we will follow these steps:

### Step 1: Prime Factorization of Each Number
1. **Prime Factorization of 64:**
- Divide 64 by 2:
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- So, the prime factorization of 64 is \(2^6\).

2. **Prime Factorization of 28:**
- Divide 28 by 2:
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 ÷ 7 = 1
- So, the prime factorization of 28 is \(2^2 \times 7\).

3. **Prime Factorization of 96:**
- Divide 96 by 2:
- 96 ÷ 2 = 48
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1
- So, the prime factorization of 96 is \(2^5 \times 3\).

### Step 2: Identify Common Factors
- Now we will look for the common prime factors among the three numbers:
- For 64: \(2^6\)
- For 28: \(2^2 \times 7\)
- For 96: \(2^5 \times 3\)

### Step 3: Determine the Lowest Power of Common Factors
- The only common prime factor is 2.
- The powers of 2 in each factorization are:
- 64: \(2^6\)
- 28: \(2^2\)
- 96: \(2^5\)
- The lowest power of 2 among these is \(2^2\).

### Step 4: Calculate the HCF
- Therefore, the HCF is \(2^2 = 4\).

### Final Answer:
The HCF of 64, 28, and 96 is **4**.

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