# Math Help - find the perfect squres!

1. ## find the perfect squres!

Compute the number of perfect squares that are factors of (5!+6!+7!)^3

2. Originally Posted by victorlui
Compute the number of perfect squares that are factors of (5!+6!+7!)^3
This is easy. Just find the number, take the square root of it, and try dividing all perfect squares smaller than that into the original total

3. All positive integers up to 5 are factors of 5! and so factors of 6! and 7! as well. Since the expression is cubed, each of those, squared, will be a perfect square dividing the expression. Also, both 2 and 3 are in 5! so 6 is a factor of 5!, 6!, and 7!. $6^2$ is also a perfect square dividing the expression.