N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

(In reply to

re: No Subject by Charlie)

Your point is well taken, Charlie; "its" requires a singular antecedent, rather than the collective set of digits as such -- so "N" is that antecedent (a string of two to four digits of which the first is not zero). Is the second sentence ("It is known that N cannot contain any LEADING zero.") otiose and just intended to mislead? Clearly if ANY of the digits of N were zero, then the product would be zero, so there would be no solution. So, all in all, ad astra...