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Plenty of onshore windfarms around the world are reaching the 20-25 year old mark and thus may be on the process of repowering.

Let's say an old wind farm has 10 rotors of 0.5 MW each (total power 10x0.5 = 5 MW). During repowering you may replace those 10 rotors by 3 larger ones of 5 MW each (total new power 3x5 = 15 MW). Therefore your repowering factor is 15/5 = 3.

These numbers are reasonable but also totally made up. In the real world, what repowering factors can you expect when replacing turbines which are for example 300 kW, 500 kW or 1 MW?

I only need an approximate number, since the end result may vary depending on the specifics for each wind farm.

Brenlla
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Wind turbune efficiency is limited to 59% by Betz law

Modern turbines are close to this limit, about 75% of optimum. Older turbines, that are also of the same type, will have almost the same efficiency, difference of only a few percent.

Larger rotor on the same tower will suffer from wind speed change with altitude. If bottom part and top part of the rotor feel different speed, it will create a tilting moment.

If you are not changing the tower, or blade's length, power will be almost the same. There is no way to make it 3 times as large on the same tower. Tower itself is limited in strength.

Largest increase in power for new designs i've seen was big nose cone, it adds 3% of power. Smoother blade surface of replaced blades can add another 5% of power.

In total I would expect new turbines to be about 10% more powerful, when installed on old towers. I dont see much potential to gain more from this replacement.

If you are replacing towers as well, you can expect more power from higher towers per area, as more altitude of wind is affected. Still, you cant expect much more, as towers will begin to shadow each other. For twice the hight I would expect about three times the power per land area. But replaced towers are unlikely to be this high.

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Larger turbines have to be spaced further apart. See Sustainable Energy Without the Hot Air by David MacKay. He gives a figure of 2 W/m2 although this may have improved a bit since his book was written.

Chapter B, The Physics of Wind Power goes into more detail.

Transistor
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