As jbfa74 suggested, go buy the exact fan and take the guts out of it. I had no idea what the original model is. So I cannot do that. I went on to look for a motor.
From ACE, with shipping, $22. Gaingers is about the same price.
Figure I stop by Lowes and Home Depot and see what they got. They have replacement motor and fan cage assembly for $25 or so. They did not have the size I needed. Apparently Broan had 7-1/4" x 7-1/2" mounting plate and 7-1/4" x 8" mounting plate. The same guts fits in all different models.
Now that I don't need to find out what EXACT model number is ..... I started to looked at new fan unit ... 50 cfm unit cost $12. 70 cfm (what I needed) cost $28. Only difference is the size of the motor and the fan cage. The guts from either will fit for my need. So for about $8 more, I can get what I need NOW without waiting.
Anyway, the bathroom where this is used is pretty tiny. So, I went the cheap way and bought the 50 cfm instead of the 70 cfm, $12 one.
In the end, I learn that the motor & fan cage is 95% of the whole new unit. Many places actually sells the motor higher price than the whole new unit!
I am surprise Broan sells the 50 & 70 cfm unit for such a big difference in price. The bigger motor cannot cost that much more.
Thanks all for your help.