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Prime Factorization and Divisors

Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic.

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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