I am trying to understand the upper bound on factorions (in base $10$). The Wikipedia page says:
"If $n$ is a natural number of $d$ digits that is a factorion, then $10^{d − 1} \le n \le 9!d$. This fails to hold for $d \ge 8$ thus $n$ has at most $7$ digits, and the first upper bound is $9,999,999$. But the maximum sum of factorials of digits for a $7$ digit number is $9!7 = 2,540,160$ establishing the second upper bound."
Please explain this to me in simple terms, precisely the first part $10^{d − 1} \le n \le 9!d$.