Let's find the prime factorization of 60 using the factor tree method, starting with the factors 30 and 2.

1. Start with the factors 30 and 2:

   • $60$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $30 \ \ \ \ \ \ \ \ \ \ 2$

2. Factor 30 further:

   • 30 can be factored into 5 and 6 (since 2 is a prime number, it's already at the end of its branch):
   • $60$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $30 \ \ \ \ \ \ \ \ \ \ 2$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $5 \ \ \ \ \ \ \ \ \ \ 6$

3. Factor 6 further:

   • 6 can be factored into 2 and 3:
   • $60$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $30 \ \ \ \ \ \ \ \ \ \ 2$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $5 \ \ \ \ \ \ \ \ \ \ 6$
   • $/ \ \ \ \ \ \ \ \ \ \ \backslash$
   • $2 \ \ \ \ \ \ \ \ \ \ 3$

4. Identify the prime numbers:

   • Now, all the branches end with prime numbers: 2, 3, and 5.

The complete factor tree looks like this:

        60
       /  \
     30    2
    /  \
   5    6
       / \
      2   3

So, the prime factorization of 60 is:

$60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5$

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the prime factorization of 30?
2. How can you confirm that 2 is a prime number?
3. How do you determine the greatest common factor using prime factorization?
4. What is the prime factorization of 90?
5. How can you use the factor tree method to simplify fractions?

Tip: When creating a factor tree, always ensure each branch ends with a prime number, as these cannot be factored further.