What are the different prime factors of 2400?

Step-by-Step Solution

To find the number of different (distinct) prime factors of 2400, we first need to perform the prime factorization of the number.

1. Break down 2400 into factors:

   • 2400 = 24 * 100

   • 24 = 8 * 3 = 2^3 * 3

   • 100 = 10 * 10 = (2 * 5) * (2 * 5) = 2^2 * 5^2

2. Combine the factors:

   • 2400 = (2^3 * 3) * (2^2 * 5^2)

   • Using the rules of exponents (adding exponents for the same base):

   • 2400 = 2^(3+2) * 3^1 * 5^2

   • 2400 = 2^5 * 3^1 * 5^2

3. Identify the distinct prime factors:

   • The prime factors present in the factorization are 2, 3, and 5.

   • Counting these, there are 3 distinct prime factors.