Calculate the number of divisors of the number 7200.

Step-by-Step Solution

1. Find Prime Factorization: First, express the number 7200 as a product of its prime factors.

   • 7200 = 72 * 100

   • 7200 = (8 * 9) * (4 * 25)

   • 7200 = (2^3 * 3^2) * (2^2 * 5^2)

   • 7200 = 2^(3+2) * 3^2 * 5^2

   • 7200 = 2^5 * 3^2 * 5^2

2. Apply the Formula for Number of Divisors: If a number n is written in the form (p^a) * (q^b) * (r^c)..., where p, q, and r are prime factors, the total number of divisors is found by taking the product of each exponent incremented by 1: (a + 1)(b + 1)(c + 1)...

3. Calculate:

   • Exponents are 5, 2, and 2.

   • Number of divisors = (5 + 1) * (2 + 1) * (2 + 1)

   • Number of divisors = 6 * 3 * 3

   • Number of divisors = 54.