Find the number of prime factor of 1024.

Options

A. 9
B. 10
C. 11
D. 12

Answer

To find the number of prime factors of 1024, we can follow these steps:

### Step 1: Prime Factorization of 1024
To start, we need to perform the prime factorization of 1024. We can do this by dividing 1024 by the smallest prime number, which is 2.

- 1024 ÷ 2 = 512
- 512 ÷ 2 = 256
- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

So, we can write:
\[ 1024 = 2^{10} \]

### Step 2: Count the Prime Factors
From the prime factorization, we see that 1024 is expressed as \( 2^{10} \). This means that the only prime factor of 1024 is 2, and it appears 10 times.

### Step 3: Determine the Number of Prime Factors
The question asks for the number of prime factors. Since 2 is the only prime factor, we have:

- Number of distinct prime factors = 1 (which is 2)

### Final Answer
Thus, the number of prime factors of 1024 is **1**.

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