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Number Theory

Prime Factorization and Divisors

Perfect Squares, Cubes and Powers


Which of the following is NOT a perfect square number?

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

Divide \(297\) by the smallest possible positive integer \(a\) so that the result is the square of a positive integer \(b\). What is \(a+b\)?

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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