CPU utilization isn't really the thing, the temperature is the reason why fans spin for the most part. Have you used any application to monitor your CPU temperatures? CoreTemp/HWiNFO/HWMonitor are good examples.
What's the laptop's make and model number? If it's older, it might be an inadequate cooler design and the thermal paste might need reapplying.
How long have you had the device? Seems like a good bang-for-the-buck device, but details are hard to find. It's not available in my country whatsoever. It seems to be a cooling issue, but I would check out the temperatures before doing anything else. The thermal paste should be good for a device under 2 years of age. Check the temperatures, if it persists and the device is still under warranty, contact your supplier for support. If they're giving you a hard time, contact HP support.
Especially if a device is under warranty, don't disassemble the device as you'll void your warranty. Since you said the fan only spins down when it's at or under 10% utilization, the only thing I can think of is a thermal issue, which will require to disassemble.