Unfortunately, it is not practical to find the number of turns in a transformer's windings. However, what matters is its turns ratio. This can be done by applying a low AC voltage to the higher-voltage* winding, and measuring the resulting voltage appearing across the lower-voltage winding. The turns ratio will be approximately the same as the voltage ratio.
(*NOT THE OTHER WAY AROUND! Or you may up with a dangerously-high voltage induced into the higher-voltage winding!)
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