The gearbox number is etched onto it, the 182's have the JC5 130 box. The earlier boxes that are in 172's are JC5 129 and JC5 089 which have a speedo drive.
You can get a second hand gearbox for around £300
Or you can get your box refurbished.
Ed.
The 182 boxes are better than the older 172 ones although still not great especially if they have been given little mechanical sympathy.
They usually whine (bearing noise) a metallic rattling noise sounds a little more concerning, could be box, diff, shafts..
If you do decide to get it...