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FALCON FW-842 8 Speed 13-42T Freewheel
#1
Can I replace the MF-TZ500-7 SHIMANO on the rear wheel (Formula DC-31 hub, alloy, 6-bolt, 6/7/8-speed freewheel) with this FALCON FW-842 8 Speed 13-42T Freewheel for my Trek Marlin 4?
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#2
Yes, as long as the threads are the same for the hub and freewheel.

7 and 8 have the same stack height, but the spacers are a little narrower to enable the extra gear.
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#3
Compatibility in bike components is crucial for proper functioning and safety
Shimano MF-TZ500-7 is a 7-speed freewheel, while the Falcon FW-842 is an 8-speed freewheel. The number of speeds must match the shifter, derailleur, and other drivetrain components. 8-speed freewheel will require a narrower chain designed for 8-speed drivetrains too
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