The RN number is not specific to the clothing. It is specific to Gymboree. "RN stands for Registered Identification Number. It is a number issued by the FTC (Federal Trade Commission) to U.S. businesses that manufacture, import, distribute, or sell products covered by the Textile, Wool, and Fur Acts. Businesses can use this number on product labels instead of the company name." https://www.ftc.gov/tips-advice/business-center/selected-industries/registered-identification-number-frequently-asked
In fact, one of the ways to spot counterfeit Gymboree is to not see the RN number to to see a different RN number than that owned by Gymboree.
There are other numbers on Gymboree clothing that are more unique. Which numbers appear on the items depends upon the year the item was produced.
Gymboree has Style Numbers (referred to as Item Numbers here on Gymboree-Lines) which are specific to a particular style made by Gymboree and Item Numbers which are specific not just to the style but to the size of the clothing item. Both of these numbers appear on Gymboree items produced in or after about 2010 -- Sorry I would have to pull some clothes out of the closet to really be sure about what year they started putting all of it on there. The Style Numbers (referred to as Item Numbers on this site) start with the number 140 and are 9 digits long. The Item Numbers start with the number 240 or more recently 241 and are also 9 digits long. On newer items (2010 and newer) both of these numbers appear on the either the front or the back of the tag.
Above those numbers there is another code that is important -- the line release code. This tells you what year the item was released, whether it is Gymboree (GY), Gymboree Outlet (GYOT), Crazy8 (C8) or Janie and Jack (JJ), and generally some other information about when the item was released.
For example, I am holding in my hand a Jewel Birds Tunic from Butterfly Garden. The RN number is there, as is the CA number (similar to the RN Number but for Canada). Then it says 16 GY FALL 3. The 16 stands for 2016. GY is for Gymboree. FALL 3 tells me that it was the third line release for Fall. All items from Butterfly Garden will have the 16 GY FALL 3 on their tags. However, more than one line is released at once, so there is more than one line with the 16 GY FALL 3 designation. I would expect some Mix N Match Playwear and GymGo items released on the same day to also have the 16 GY FALL 3 on their tags.
140 numbers are sequential but they are assigned to a style when the style is first being designed by Gymboree. So sequential 140 numbers may be from the same line or from two different lines that were developed at the same time. You can search for an item on Gymboree-Lines using its 140 number.
240 and 241 numbers are sequential too. This Butterfly Garden tunic has the number 241628645 and is a Medium (7/8). Based on that I know that the Large (10/12) will have number 241629646 and that the Small (5/6) will have the number 241629644.
Older lines like Fall Forest and Pretty in Plum will only have the 240 number on their tags, not the 140 number. Some of these numbers have been entered into our database here as keywords to make them searchable, but we do not have all of the 240 numbers because they were not part of the original info that came from the Gymboree website. You can try searching a 240 number but it may not give you results. You can also search for a partial 240 number. For example, if I wanted to search a partial 240 number I would type as much of it as I wanted to and then add an asterisk to the end of the number. That tells the system to give me everything that starts with that number string. That might give you some results. I have a Fall Forest dress here that is number 240458770. That is a number specific to this dress in size 7. If I put in the number 24045* I get a list of results. This dress is there, as are two other items from Fall Forest.
Another tidbit about 240 and 241 numbers -- they are the numbers that appear on your receipt from Gymboree. They use those numbers for inventory control because that number indicates that a piece in a style and particular size was sold. But it is the 140 number that you need when you are trying to get them to look something up for you or to search on the website.
Really vintage Gymboree like Hide N Seek or Fox Trot will have still different numbers on their tags. In that era, Gymboree had one set of style numbers for Baby Girl, one for Kid Girl, and a third one for accessories. 15 numbers were 9 digits long and were Baby Girl numbers. Kid Girl numbers started with 5 and were only 8 digits long. Accessories numbers started with 2 and were 8 digits long. Numbers from that time frame had a / and a 99 number at the end that indicated the size of the item. Those numbers are also searchable on Gymboree-Lines, but we don't have all of them in the system. You can use the * trick on those numbers too. For example, if I search 52801*, I get results from a bunch of lines released in the summer and fall of 2004.
Still older Gymboree will have a year on it but no style/item number. Super vintage Gymboree will not even have a year on it.
I know that was more than you asked, but I hope it has helped to demystify your Gymboree tags a bit. 
