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Problem of the Week
Problem D
Squares in a Square

The prime factorization of \(20\) is \(2^2\times 5\).

The number \(20\) has \(6\) positive divisors. They are:

\(2^05^0=1\)\(2^05^1=5\)\(2^15^0=2\)\(2^15^1=10\)\(2^25^0=4\),  \(2^25^1=20\)

Two of the divisors, \(1\) and \(4\), are perfect squares.

How many positive divisors of \(36^3\) are perfect squares?