Cute question.
Break down 2700 to is prime factors:
2700 = 27*100 = 3^3 * 2^2 * 5^2
from here, it's a matter of finding all the different combinations of prime factors that can come under the heading "^2":
divisors with one prime factor:
3^2 = 9
2^2 = 4
5^2 = 25
Divisors with two prime factors:
(2*3)^2 = 6^2 = 36
(2*5)^2 = 10^2 = 100
(3*5)^2 = 15^2 = 225
Divisors with three prime factors:
(2*3*5)^2 = 30^2 = 900
One last important divisor that is easily forgotten, and is thus the trick of the question: 1^2 is also a perfect square.
Total number of divisors that are perfect squares: 8.
Divisibility / Squares
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