To find the greatest perfect square that is a factor of 756, we first find the factors of 756.
Factors of 756 are: 1,2,3,4,6,7,9,12,14,18,21,27,28,36,42,54,63,84,108,126,189,252,378,756
Now we start to find the perfect square from the greatest factors;
756 = not perfect square
378 = not perfect square
252 = not perfect square
189 = not perfect square
126 =not perfect square
108 =not perfect square
84 = not perfect square
63 = not perfect square
54 = not perfect square
42 = not perfect square
36 = perfect square = 6 x 6 = 6² = 36
So, 36 is the greatest perfect square from the factors of 756.