For any positive integer $n$, the value of $n!$ is the product of the first $n$ positive integers.  For example, $4! = 4\cdot 3\cdot 2\cdot 1 =24$.  What is the greatest common divisor of $5!$ and $7!$ ?
I notice that $7!$ is just $7\cdot 6\cdot 5!$, so $5!$ is a factor of $7!$. That means that $5!$ is the greatest common divisor of $5!$ and $7!$, since it is the largest factor of both numbers. To find $5!$, I just need to multiply the first five positive integers: $5! = 5\cdot 4\cdot 3\cdot 2\cdot 1 = 120$. 