How many proper divisors (that is, divisors other than 1 or 7200) does 7200 have?

To find the number of factors of a number $N = p^{a} × q^{b} × r^{c}$

The formula is: $(a+1)(b+1)(c+1)$

where $a,b,c$ are powers in prime factorization and $p,q,r$ are prime numbers

For 7200:

Prime factorization = $2^5 × 3^2 × 5^2$

Total number of factors:

$(5+1)(2+1)(2+1)$

$= 6 × 3 × 3$

$= 54$ factors

Proper divisors exclude 1 and the number itself

Therefore, number of proper divisors = $54 - 2 = 52$

The answer is $52.$