The model number for your fan is a 5-digit number that may also include a letter at the end (e.g. 22345A). You will find it on the parts guide that was included with your fan, on the box itself, or on the gold sticker on top of the fan motor (facing the ceiling of an installed fan). To make it easier to read the model number on the motor once installed, hold a small mirror above the fan facing the sticker or just take a picture with your phone!
However, for low profile fans, the sticker is on the mounting bracket.