Question

What is the greatest perfect square that is a factor of 4536

Answer 1

The greatest perfect square factor of 4536 is 324.

Solution:

Given, number is 4536

We have to find the greatest perfect square that is a factor of 4536.

Now, let us factorize the above number.

`\begin{array}{l}{4536=2268 * 2} \\\\ {=1134 * 2 * 2} \\\\ {=567 * 2 * 2} \\\\ {=189 * 2 * 2^(2)} \\\\ {=63 * 3 * 2 * 2^(2)} \\\\ {=21 * 3 * 3^(2) * 2 * 2^(2)} \\\\ {=7 * 3^(2) * 3^(2) * 2 * 2^(2)} \\\\ {=7 * 2 *(3 * 3 * 2)^(2)} \\\\ {=14 * 18^(2)}\end{array}`

So, greatest perfect square is
`18^2` = 324

Hence, the greatest perfect square factor of 4536 is 324.