Number of Perfect Cube Factors in 4500
The first step to determine the number of perfect cube factors in 4500 is to prime factorize the number.

Prime Factorization of 4500:
- 4500 = 2 * 2 * 3 * 3 * 5 * 5 * 5

Identifying Perfect Cube Factors:
- To find perfect cube factors, we need to look for groups of three identical prime factors in the prime factorization.
- In the prime factorization of 4500, we have two sets of three identical prime factors: 2 * 2 * 2 and 3 * 3 * 3.

Calculating Perfect Cube Factors:
- To find the perfect cube factors, we count the number of sets of three identical prime factors.
- In this case, we have two sets: 2 * 2 * 2 and 3 * 3 * 3.

Number of Perfect Cube Factors in 4500:
- Therefore, the number of perfect cube factors in 4500 is 2.
In conclusion, 4500 has 2 perfect cube factors, which are 8 (2 * 2 * 2) and 27 (3 * 3 * 3).