The number of factors 48 is

Options

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

Answer

To find the number of factors of 48, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of 48.

- 48 can be divided by 2 (the smallest prime number):
\[ 48 \div 2 = 24 \]
- 24 can also be divided by 2:
\[ 24 \div 2 = 12 \]
- 12 can also be divided by 2:
\[ 12 \div 2 = 6 \]
- 6 can also be divided by 2:
\[ 6 \div 2 = 3 \]
- 3 is a prime number and cannot be divided further.

So, the prime factorization of 48 is:
\[ 48 = 2^4 \times 3^1 \]

### Step 2: Use the Formula for Finding the Number of Factors
The formula to find the number of factors from the prime factorization \( p_1^{e_1} \times p_2^{e_2} \times \ldots \times p_n^{e_n} \) is:
\[ (e_1 + 1)(e_2 + 1) \ldots (e_n + 1) \]
where \( e_1, e_2, \ldots, e_n \) are the exponents in the prime factorization.

For 48, we have:
- \( e_1 = 4 \) (from \( 2^4 \))
- \( e_2 = 1 \) (from \( 3^1 \))

Using the formula:
\[ (4 + 1)(1 + 1) = 5 \times 2 = 10 \]

### Conclusion
Thus, the total number of factors of 48 is **10**.

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