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 \(x?\)
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.