How many positive divisors of 10800 are perfect squares?

$10800=2^4\cdot 3^3\cdot 5^2$. A square divisor needs even powers: 2 → 0, 2, 4 (3 ways); 3 → 0, 2 (2 ways); 5 → 0, 2 (2 ways). $3\times 2\times 2=12$. (60 counts all divisors.)