Number Theory
# Prime Factorization and Divisors

Which of the following is NOT a perfect square number?

If \(270x\) is a perfect square, what is the smallest possible integer value of \(x?\)

Find the smallest positive integer \( c \) that satisfies

\[ 360a = 1500b = c^2, \]

where \(a\) and \(b\) are positive integers.

Find the largest 4-digit positive integer which is a perfect power of 2.

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