To determine how many factors 30 has, we can follow these steps:

Step 1: Prime Factorization

First, express 30 as a product of prime factors: $30 = 2 \times 3 \times 5$ This is the prime factorization of 30.

Step 2: Use the Formula for the Number of Factors

If a number $n$ has the prime factorization: $n = p_1^{e_1} \times p_2^{e_2} \times \dots \times p_k^{e_k}$ where $p_1, p_2, \dots, p_k$ are distinct primes and $e_1, e_2, \dots, e_k$ are their respective exponents, the number of factors of $n$ is given by: $(e_1 + 1)(e_2 + 1) \dots (e_k + 1)$

For 30, the prime factorization is: $30 = 2^1 \times 3^1 \times 5^1$ So, the number of factors is: $(1 + 1)(1 + 1)(1 + 1) = 2 \times 2 \times 2 = 8$

Conclusion

The number of factors of 30 is 8.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What are all the factors of 30?
2. How do you find the greatest common divisor (GCD) of 30 and another number?
3. What is the least common multiple (LCM) of 30 and 45?
4. How many prime factors does 60 have?
5. How can prime factorization be used in simplifying fractions?

Tip: The sum of the exponents in a prime factorization tells you about the divisibility properties of a number.