The number of factors of 60 are

Options

A. 10
B. 12
C. 14
D. 15

Answer

To find the number of factors of the number 60, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of 60.

- Start by dividing 60 by the smallest prime number, which is 2:
\[ 60 \div 2 = 30 \]
- Divide 30 by 2 again:
\[ 30 \div 2 = 15 \]
- Now, divide 15 by the next smallest prime number, which is 3:
\[ 15 \div 3 = 5 \]
- Finally, 5 is a prime number itself.

So, the prime factorization of 60 is:
\[ 60 = 2^2 \times 3^1 \times 5^1 \]

### Step 2: Use the Formula for Counting Factors
To find the total number of factors, we 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.

From the prime factorization \(60 = 2^2 \times 3^1 \times 5^1\):
- The exponent of 2 is 2.
- The exponent of 3 is 1.
- The exponent of 5 is 1.

Now, applying the formula:
\[ \text{Number of factors} = (2 + 1)(1 + 1)(1 + 1) \]
\[ = 3 \times 2 \times 2 \]
\[ = 12 \]

### Conclusion
Thus, the total number of factors of 60 is 12.