Question

How many factors of $7560$ are perfect square?

Answer 1

Estimate the perfect squares:

The given number is,

$7560=1\times 2^3\times 3^3\times 5\times 7$

$=1^2\times \left(2^2\right)2\times \left(3^2\right)3\times 5\times 7$

$={\left(2\times 3\right)}^2\times 2\times 3\times 5\times 7$

$=6^2\times 2\times 2\times 5\times 7$

Therefore, from these given representations, we can estimate the perfect squares, that are

$1^2,2^2,3^2,6^2=1,4,9,36$

Hence, there are $4$ perfect squares among the factors of $7560$.