The number of factors of 640 is

Options

A. 20
B. 16
C. 23
D. 24

Answer

To find the number of factors of the number 640, we can follow these steps:

### Step 1: Prime Factorization of 640
First, we need to perform the prime factorization of 640.

1. Divide 640 by 2 (the smallest prime number):
\[ 640 \div 2 = 320 \]
2. Divide 320 by 2:
\[ 320 \div 2 = 160 \]
3. Divide 160 by 2:
\[ 160 \div 2 = 80 \]
4. Divide 80 by 2:
\[ 80 \div 2 = 40 \]
5. Divide 40 by 2:
\[ 40 \div 2 = 20 \]
6. Divide 20 by 2:
\[ 20 \div 2 = 10 \]
7. Divide 10 by 2:
\[ 10 \div 2 = 5 \]
8. Finally, 5 is a prime number.

Thus, the prime factorization of 640 is:
\[ 640 = 2^7 \times 5^1 \]

### Step 2: Use the Formula to Find the Number of Factors
To find the total number of factors of a number from its prime factorization, we can use the formula:
\[ \text{Number of factors} = (e_1 + 1)(e_2 + 1)(e_3 + 1) \ldots \]
where \(e_1, e_2, e_3, \ldots\) are the exponents in the prime factorization.

For 640:
- The exponent of 2 is 7.
- The exponent of 5 is 1.

So, we apply the formula:
\[ \text{Number of factors} = (7 + 1)(1 + 1) = 8 \times 2 = 16 \]

### Conclusion
Thus, the number of factors of 640 is **16**.