what differentiates in 2/12 way and 3 way speaker ?

I have heard 21/2 way speakers that's sounding better than a 3 way speakers.  How the crossover is working differently ?  Is it easier for an integrated amp to power a 21/2 way ?  Is the sound is more linear than a 3 way speaker ?  How an integrated amp can get 1000 of Damping Factor ?  Is a greater Damping Facor is giving a better sound to a 92 dB speaker ?

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I don’t know and would be interested too. A three way has three drivers and a 2 1/2 way have 3 drivers. On a 2 1/2 way is the bottom driver crossed over as a sub?

Years ago I owned a 2 and 1/2 way Spendor and it was outstanding. Here is how that design works

A 2 and 1/2 way design refers to two (or more) drivers covering the same region with each driver having a different cutoff frequency. This is most often done in the lower frequencies. If the cabinet contains two 8" low frequency drivers both will operate from the low frequency limit and upward. One of the two 8" drivers will roll off at 250Hz or so, therefore it is supplementing only the lowest few octaves. Both drivers handle the same extreme low frequencies but both do not handle all the same upper frequencies.

yogiboy, thank you for your answer I appreciate.  Yes: 1 tweeter, one mid and 2 woofers.

3 way = separate driver (or set of drivers) for treble, mid, and bass.
2.5 way = separate driver for treble, another driver that handles mid and bass, and separate driver for bass.

The simple differences are the 3-way separates the frequencies into separate drivers. and the 2.5 way gives you two drivers to deliver the bass.

3 way has a woofer mid woofer and tweeter, 3 way crossover.

Yes mostly, but it is a 3 way crossover design driving at least 3 drivers. It could have any number of drivers and still be a 3 way loudspeaker. A one-half way loudspeaker is when there are two (or more) drivers that operate in the same frequency range at some portions of the band but are cut off at different frequencies. It's a fine point though because it would still have a 3 way crossover. 

The 2 1/2 way is missing a high pass filter on what would normally be the midrange.

That’s the missing 1/2 component.

The advantages of 2 1/2 way speakers is usually having a small footprint but increased sensitivity, with some tradeoffs often occurring in the impedance being lower than it might be with a 3 way.

I’ve posted a thread here before that for many people the 2 1/2 way speaker may be ideal. Small, high output, deep bass.