数 and 番号
 

If I'm referring to "product number 3" but want to shorten it to just "number 3" - would it be proper to use 数 (kazu) or 番号 (bangou)?

Product Number 3 - 商品３番, number 3 - ３番

数（かず） means a number, it cannot be used as a counter.
番号 means a number that is assigned to the counter. e.g. この商品の番号は３です。But it cannot be used as a counter either.

Looks like I had the wrong idea entirely. Thanks!