Find the number of factor of 80.

Options

A. 10
B. 12
C. 6
D. 8

Answer

To find the number of factors of the number 80, we will follow these steps:

### Step 1: Prime Factorization of 80
First, we need to perform the prime factorization of 80. We can divide 80 by the smallest prime number, which is 2.

- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 ÷ 5 = 1

So, the prime factorization of 80 is:
\[ 80 = 2^4 \times 5^1 \]

### Step 2: Use the Formula to Find the Number of Factors
The formula to find the number of factors of a number based on its prime factorization \( p_1^{e_1} \times p_2^{e_2} \) is:
\[ (e_1 + 1)(e_2 + 1) \]

In our case:
- For \( 2^4 \), the exponent \( e_1 = 4 \)
- For \( 5^1 \), the exponent \( e_2 = 1 \)

### Step 3: Calculate the Number of Factors
Now, we can substitute the values into the formula:
\[ (4 + 1)(1 + 1) \]
\[ = 5 \times 2 \]
\[ = 10 \]

### Conclusion
Thus, the number of factors of 80 is **10**.

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