Factoring Factorials (Source: Mathcounts)

$7!=6! \times 7=>7!+6!=6!(1+7)=6! \times 8=>\frac{(7!+6!)}{8}=\frac {6! \times 8}{8}=6!=720$

$\color{midnightblue}{\frac{7!+6!}{8}=\frac{6!(7+1)}{8}=\frac{6!\times8}{8}=6!=\boxed{720}}$

$\frac{7!+6!}{8}=\frac{(1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7)+(1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6)}{8}=\frac{5760}{8}=\mathbf{720}$