Answer:
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.
[tex]\begin{array}{l}{4536=2268 \times 2} \\\\ {=1134 \times 2 \times 2} \\\\ {=567 \times 2 \times 2} \\\\ {=189 \times 2 \times 2^{2}} \\\\ {=63 \times 3 \times 2 \times 2^{2}} \\\\ {=21 \times 3 \times 3^{2} \times 2 \times 2^{2}} \\\\ {=7 \times 3^{2} \times 3^{2} \times 2 \times 2^{2}} \\\\ {=7 \times 2 \times(3 \times 3 \times 2)^{2}} \\\\ {=14 \times 18^{2}}\end{array}[/tex]
So, greatest perfect square is [tex]18^2[/tex] = 324
Hence, the greatest perfect square factor of 4536 is 324.
