The number of factors of 24 is _________

Options

A. 7
B. 8
C. 6
D. 5

Explanation

To find the number of factors of the number 24, we can follow these steps:

### Step 1: Find the prime factorization of 24.
To do this, we can divide 24 by the smallest prime numbers until we reach 1.

- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1

So, the prime factorization of 24 is:
\[ 24 = 2^3 \times 3^1 \]

### Step 2: Use the formula for finding the number of factors.
The formula for finding the number of factors from the prime factorization is:
If \( n = p_1^{e_1} \times p_2^{e_2} \times ... \times p_k^{e_k} \), then the number of factors \( d(n) \) is given by:
\[ d(n) = (e_1 + 1)(e_2 + 1)...(e_k + 1) \]

In our case:
- For \( 2^3 \), \( e_1 = 3 \)
- For \( 3^1 \), \( e_2 = 1 \)

So, applying the formula:
\[ d(24) = (3 + 1)(1 + 1) \]
\[ d(24) = 4 \times 2 \]

### Step 3: Calculate the total number of factors.
Now we can calculate:
\[ d(24) = 4 \times 2 = 8 \]

### Conclusion:
The number of factors of 24 is **8**.

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