"Obviously" begins a statement that continues "the factorion of an n-digit number cannot exceed n. 9!" (the dot expresses "n times 9!").

One way to see what this is about is linguistic. "Obviously" is a way of saying "I see ... and you could (if ...)". For most of the world the second ... is interpreted as something like "you thought about it."

Thinking is not easy. People prefer "seeing"; they dislike things they must think about (even when they're fairly easy).

This "obviously" is very easy: There are n integers. The biggest each can be is 9. The factorion is the sum of the factorials of the digits. The most we can get by adding up n factorials is n times 9! Let's see what that means numerically.

9! is 9(8)7(6)5!

5! = 5(4!) = 20(3)2 = 120

9! = 72(42)120 = 362,880

If a number has n-many digits, n times 362,880 must be examined (to find if this n-digit number is a sum of factorials of its digits).