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tep 1
The quickest way to tell whether your PS3 can play PS2 games is to look at the number of USB ports on the front of the console. If your PS3 has 4 USB ports, it's probably (but not always!) a model with backwards compatibility for PS2 games. However, if your PS3 has 2 USB ports, it is NOT backwards compatible.
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Step 2
Check the back of the console for more precise information about your model. On the back, there will be a label which includes your PS3's model number. This model number begins with the letters "CECH".
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Step 3
You have backwards compatibility for PS2 games if your PS3 has a model number beginning in CECHA, CECHB, CECHC, or CECHE. All other models are incapable of running PS2 software.
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Step 4
Furthermore, these four model numbers can be further divided by the type of PS2 support they provide. CECHA and CECHB models include special hardware that allows PS2 games to run exactly how they would run on an actual PS2.
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Step 5
CECHC and CECHE model numbers, however, use software emulation to play PS2 games. This means that support for PS2 software is imperfect. You may run into glitches when playing some PS2 games on these consoles.