How many perfect squares divide the number 4!·5!·6!?

4! = 24

The perfect square factors of 4! are 1 and 4.

5! = 120

The perfect square factors of 5! are 1 and 4.

6! = 720

The perfect square factors of 6! are 1, 4, 9, 16, 36, and 144.

Those are the perfect square factors of the big product as well:

1, 4, 9, 16, 36, and 144.