(x+1)! = 720
Descompunem pe 720 in factori primi.
[tex]720 = 2^4 \times 3^2 \times 5 [/tex]
Reorganizam factorii pentru a obtine un factorial.
[tex]720 = 1 \times 2 \times 3 \times 2^2 \times 5 \times (2 \times 3) \\
720 = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \\
\Longrightarrow~~720 = 6! \\ \\
(x+1)! = 6! \\
x+1 = 6 \\
x = 6-1 = \boxed{5}[/tex]
