What is the HCF of 16 and 32?

Options

A. 4
B. 12
C. 16
D. 20

Answer

To find the Highest Common Factor (HCF) of 16 and 32, we can follow these steps:

### Step 1: Factor the numbers
First, we need to factor both numbers into their prime factors.

- **For 16**:
- 16 can be divided by 2:
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- So, the prime factorization of 16 is:
\[ 16 = 2 \times 2 \times 2 \times 2 = 2^4 \]

- **For 32**:
- 32 can also be divided by 2:
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- So, the prime factorization of 32 is:
\[ 32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5 \]

### Step 2: Identify the common factors
Next, we identify the common factors from the prime factorizations:
- The prime factors of 16 are \(2^4\).
- The prime factors of 32 are \(2^5\).

### Step 3: Determine the HCF
The HCF is found by taking the lowest power of the common prime factors:
- The common prime factor is 2.
- The lowest power of 2 in both factorizations is \(2^4\).

Thus, the HCF of 16 and 32 is:
\[ HCF = 2^4 = 16 \]

### Final Answer
Therefore, the HCF of 16 and 32 is **16**.

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