There are other causes such as setting input gain incorrectly. For example... imagine you are one foot from the microphone... the volume of your voice reaching the microphone is what you are looking for etc... now place the singer three feet from the microphone... to get the recorded signal up so that it achieves a similar recording level for yhe voice either the singer sings louder OR you turn up input gain... the trouble is that in amplifying the signal to the same level the ambient noise is now also boosted.... ie the Signal to Noise Ratio (SNR) is now a hell of a lot worse.
you can improve your situation by using a more sensitive microphone, and better Analog to Digital Converters (ADC), closer microphone positioning, generally quieter circuitry, placing your mic in a different room from your computer and othet (fan noise etc) and by careful cable routing ( though that is more to reduce crosstalk between cables) etc. Closer positioning can also bring in to play "proximity effect" (boosted bass) depending on your mic and microphone pop (use a pop blast screen - buy or cheaply make your own. My first home pop screen was made with stockings/hose and metal coat hanger lol
on the subject of cable noise make sure your audio cables are as isolated as possible to reduce noise of varios kinds. particularly as far as possible from mains/grid power cables and digital cables, including midi).
yes you can use denoiser software/hardware but you WILL colour the original sound to. While it can be done to an acceptable level, prevention is better than cure. Something to also consider is the use of a high shelf Eq but that too will also colour your sound.